LMFDB - Embedded newform 690.2.q.a.11.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(11,690)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 0, 9]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("690.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.q (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$16$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			11.14
Character	$\chi$	$=$	690.11
Dual form			690.2.q.a.251.14

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.540641 + 0.841254i) q^{2} +(0.843944 + 1.51253i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.816154 + 1.52771i) q^{6} +(-1.57741 + 1.36683i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(-1.57552 + 2.55299i) q^{9} +O(q^{10})$	\(q+(0.540641 + 0.841254i) q^{2} +(0.843944 + 1.51253i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.816154 + 1.52771i) q^{6} +(-1.57741 + 1.36683i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(-1.57552 + 2.55299i) q^{9} +(-0.755750 - 0.654861i) q^{10} +(3.18184 + 2.04484i) q^{11} +(-1.72644 + 0.139349i) q^{12} +(0.684999 - 0.790531i) q^{13} +(-2.00266 - 0.588035i) q^{14} +(-1.23589 - 1.21350i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(0.274598 + 0.601286i) q^{17} +(-2.99950 + 0.0548407i) q^{18} +(-0.675988 - 0.308713i) q^{19} +(0.142315 - 0.989821i) q^{20} +(-3.39862 - 1.23235i) q^{21} +3.78226i q^{22} +(-4.76620 - 0.532257i) q^{23} +(-1.05061 - 1.37703i) q^{24} +(0.841254 - 0.540641i) q^{25} +(1.03538 + 0.148865i) q^{26} +(-5.19113 - 0.228443i) q^{27} +(-0.588035 - 2.00266i) q^{28} +(-6.52326 + 2.97907i) q^{29} +(0.352688 - 1.69576i) q^{30} +(-0.806093 - 5.60650i) q^{31} +(0.281733 - 0.959493i) q^{32} +(-0.407600 + 6.53837i) q^{33} +(-0.357375 + 0.556086i) q^{34} +(1.12843 - 1.75587i) q^{35} +(-1.66779 - 2.49369i) q^{36} +(1.03825 - 3.53595i) q^{37} +(-0.105760 - 0.735580i) q^{38} +(1.77381 + 0.368920i) q^{39} +(0.909632 - 0.415415i) q^{40} +(3.40974 + 11.6125i) q^{41} +(-0.800713 - 3.52537i) q^{42} +(6.27140 + 0.901692i) q^{43} +(-3.18184 + 2.04484i) q^{44} +(0.792437 - 2.89345i) q^{45} +(-2.12904 - 4.29735i) q^{46} -2.65181i q^{47} +(0.590431 - 1.62831i) q^{48} +(-0.376217 + 2.61665i) q^{49} +(0.909632 + 0.415415i) q^{50} +(-0.677719 + 0.922790i) q^{51} +(0.434534 + 0.951496i) q^{52} +(4.00210 + 4.61867i) q^{53} +(-2.61436 - 4.49056i) q^{54} +(-3.62905 - 1.06558i) q^{55} +(1.36683 - 1.57741i) q^{56} +(-0.103557 - 1.28299i) q^{57} +(-6.03290 - 3.87711i) q^{58} +(6.87698 + 5.95894i) q^{59} +(1.61724 - 0.620098i) q^{60} +(11.8254 - 1.70023i) q^{61} +(4.28068 - 3.70923i) q^{62} +(-1.00427 - 6.18057i) q^{63} +(0.959493 - 0.281733i) q^{64} +(-0.434534 + 0.951496i) q^{65} +(-5.72079 + 3.19201i) q^{66} +(-1.86860 - 2.90760i) q^{67} -0.661021 q^{68} +(-3.21735 - 7.65824i) q^{69} +2.08721 q^{70} +(5.63612 + 8.76998i) q^{71} +(1.19615 - 2.75122i) q^{72} +(4.81545 - 10.5444i) q^{73} +(3.53595 - 1.03825i) q^{74} +(1.52771 + 0.816154i) q^{75} +(0.561631 - 0.486656i) q^{76} +(-7.81401 + 1.12348i) q^{77} +(0.648637 + 1.69167i) q^{78} +(4.94711 + 4.28670i) q^{79} +(0.841254 + 0.540641i) q^{80} +(-4.03550 - 8.04455i) q^{81} +(-7.92562 + 9.14666i) q^{82} +(-1.44461 - 0.424176i) q^{83} +(2.53283 - 2.57956i) q^{84} +(-0.432877 - 0.499566i) q^{85} +(2.63203 + 5.76333i) q^{86} +(-10.0112 - 7.35248i) q^{87} +(-3.44046 - 1.57121i) q^{88} +(-1.15319 + 8.02060i) q^{89} +(2.86255 - 0.897676i) q^{90} +2.18327i q^{91} +(2.46411 - 4.11438i) q^{92} +(7.79972 - 5.95081i) q^{93} +(2.23085 - 1.43368i) q^{94} +(0.735580 + 0.105760i) q^{95} +(1.68903 - 0.383629i) q^{96} +(4.53637 + 15.4495i) q^{97} +(-2.40466 + 1.09817i) q^{98} +(-10.2335 + 4.90151i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9}+O(q^{10}) $ 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9	$ 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9} - 12 q^{11} - 12 q^{14} - 16 q^{16} - 8 q^{18} + 16 q^{20} + 62 q^{21} + 4 q^{23} + 2 q^{24} - 16 q^{25} + 42 q^{27} - 2 q^{30} - 4 q^{31} + 16 q^{33} + 2 q^{36} + 72 q^{38} - 124 q^{39} + 44 q^{41} + 44 q^{43} + 12 q^{44} - 2 q^{45} + 4 q^{46} + 70 q^{49} - 2 q^{51} - 52 q^{53} + 92 q^{54} + 10 q^{55} - 54 q^{56} - 38 q^{57} - 36 q^{58} - 44 q^{61} - 220 q^{63} + 16 q^{64} - 34 q^{66} - 44 q^{67} + 22 q^{69} - 12 q^{70} - 36 q^{72} - 28 q^{73} - 24 q^{74} - 88 q^{77} - 54 q^{78} - 44 q^{79} - 16 q^{80} - 66 q^{81} - 28 q^{82} + 4 q^{83} - 18 q^{84} + 158 q^{86} - 64 q^{87} + 80 q^{89} - 8 q^{90} - 4 q^{92} + 4 q^{93} + 24 q^{94} - 2 q^{96} - 88 q^{98} + 190 q^{99}+O(q^{100}) $ 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9 - 12 * q^11 - 12 * q^14 - 16 * q^16 - 8 * q^18 + 16 * q^20 + 62 * q^21 + 4 * q^23 + 2 * q^24 - 16 * q^25 + 42 * q^27 - 2 * q^30 - 4 * q^31 + 16 * q^33 + 2 * q^36 + 72 * q^38 - 124 * q^39 + 44 * q^41 + 44 * q^43 + 12 * q^44 - 2 * q^45 + 4 * q^46 + 70 * q^49 - 2 * q^51 - 52 * q^53 + 92 * q^54 + 10 * q^55 - 54 * q^56 - 38 * q^57 - 36 * q^58 - 44 * q^61 - 220 * q^63 + 16 * q^64 - 34 * q^66 - 44 * q^67 + 22 * q^69 - 12 * q^70 - 36 * q^72 - 28 * q^73 - 24 * q^74 - 88 * q^77 - 54 * q^78 - 44 * q^79 - 16 * q^80 - 66 * q^81 - 28 * q^82 + 4 * q^83 - 18 * q^84 + 158 * q^86 - 64 * q^87 + 80 * q^89 - 8 * q^90 - 4 * q^92 + 4 * q^93 + 24 * q^94 - 2 * q^96 - 88 * q^98 + 190 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$-1$	$e\left(\frac{9}{22}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.540641	+	0.841254i	0.382291	+	0.594856i
$2$	0.540641	+	0.841254i	0.382291	+	0.594856i
$3$	0.843944	+	1.51253i	0.487251	+	0.873262i
$3$	0.843944	+	1.51253i	0.487251	+	0.873262i
$4$	−0.415415	+	0.909632i	−0.207708	+	0.454816i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$6$	−0.816154	+	1.52771i	−0.333193	+	0.623684i
$7$	−1.57741	+	1.36683i	−0.596204	+	0.516614i	−0.899866	−	0.436166i	$-0.856336\pi$
$7$	−1.57741	+	1.36683i	−0.596204	+	0.516614i	0.303662	+	0.952780i	$0.401791\pi$
$8$	−0.989821	+	0.142315i	−0.349955	+	0.0503159i
$9$	−1.57552	+	2.55299i	−0.525172	+	0.850996i
$10$	−0.755750	−	0.654861i	−0.238989	−	0.207085i
$11$	3.18184	+	2.04484i	0.959360	+	0.616543i	0.923821	−	0.382825i	$-0.125049\pi$
$11$	3.18184	+	2.04484i	0.959360	+	0.616543i	0.0355388	+	0.999368i	$0.488685\pi$
$12$	−1.72644	+	0.139349i	−0.498379	+	0.0402267i
$13$	0.684999	−	0.790531i	0.189985	−	0.219254i	−0.652764	−	0.757561i	$-0.726391\pi$
$13$	0.684999	−	0.790531i	0.189985	−	0.219254i	0.842749	+	0.538307i	$0.180936\pi$
$14$	−2.00266	−	0.588035i	−0.535234	−	0.157159i
$15$	−1.23589	−	1.21350i	−0.319105	−	0.313324i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	0.274598	+	0.601286i	0.0665998	+	0.145833i	0.940005	−	0.341162i	$-0.110820\pi$
$17$	0.274598	+	0.601286i	0.0665998	+	0.145833i	−0.873405	+	0.486995i	$0.838093\pi$
$18$	−2.99950	+	0.0548407i	−0.706989	+	0.0129261i
$19$	−0.675988	−	0.308713i	−0.155082	−	0.0708237i	0.336362	−	0.941733i	$-0.390804\pi$
$19$	−0.675988	−	0.308713i	−0.155082	−	0.0708237i	−0.491444	+	0.870909i	$0.663531\pi$
$20$	0.142315	−	0.989821i	0.0318226	−	0.221331i
$21$	−3.39862	−	1.23235i	−0.741641	−	0.268922i
$22$			3.78226i			0.806380i
$23$	−4.76620	−	0.532257i	−0.993822	−	0.110983i
$23$	−4.76620	−	0.532257i	−0.993822	−	0.110983i
$24$	−1.05061	−	1.37703i	−0.214455	−	0.281086i
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	1.03538	+	0.148865i	0.203054	+	0.0291947i
$27$	−5.19113	−	0.228443i	−0.999033	−	0.0439638i
$28$	−0.588035	−	2.00266i	−0.111128	−	0.378468i
$29$	−6.52326	+	2.97907i	−1.21134	+	0.553200i	−0.915608	−	0.402071i	$-0.868290\pi$
$29$	−6.52326	+	2.97907i	−1.21134	+	0.553200i	−0.295731	+	0.955271i	$0.595563\pi$
$30$	0.352688	−	1.69576i	0.0643918	−	0.309602i
$31$	−0.806093	−	5.60650i	−0.144779	−	1.00696i	−0.924596	−	0.380950i	$-0.875597\pi$
$31$	−0.806093	−	5.60650i	−0.144779	−	1.00696i	0.779817	−	0.626007i	$-0.215312\pi$
$32$	0.281733	−	0.959493i	0.0498038	−	0.169616i
$33$	−0.407600	+	6.53837i	−0.0709541	+	1.13818i
$34$	−0.357375	+	0.556086i	−0.0612893	+	0.0953680i
$35$	1.12843	−	1.75587i	0.190740	−	0.296797i
$36$	−1.66779	−	2.49369i	−0.277964	−	0.415615i
$37$	1.03825	−	3.53595i	0.170687	−	0.581306i	−0.829068	−	0.559149i	$-0.811128\pi$
$37$	1.03825	−	3.53595i	0.170687	−	0.581306i	0.999754	−	0.0221579i	$-0.00705367\pi$
$38$	−0.105760	−	0.735580i	−0.0171566	−	0.119327i
$39$	1.77381	+	0.368920i	0.284036	+	0.0590745i
$40$	0.909632	−	0.415415i	0.143825	−	0.0656829i
$41$	3.40974	+	11.6125i	0.532512	+	1.81357i	0.579893	+	0.814693i	$0.303094\pi$
$41$	3.40974	+	11.6125i	0.532512	+	1.81357i	−0.0473805	+	0.998877i	$0.515087\pi$
$42$	−0.800713	−	3.52537i	−0.123553	−	0.543976i
$43$	6.27140	+	0.901692i	0.956380	+	0.137507i	0.602795	−	0.797896i	$-0.294053\pi$
$43$	6.27140	+	0.901692i	0.956380	+	0.137507i	0.353585	+	0.935402i	$0.384963\pi$
$44$	−3.18184	+	2.04484i	−0.479680	+	0.308271i
$45$	0.792437	−	2.89345i	0.118130	−	0.431330i
$46$	−2.12904	−	4.29735i	−0.313910	−	0.633609i
$47$		−	2.65181i		−	0.386807i	−0.981119	−	0.193403i	$-0.938047\pi$
$47$		−	2.65181i		−	0.386807i	0.981119	−	0.193403i	$-0.0619526\pi$
$48$	0.590431	−	1.62831i	0.0852213	−	0.235026i
$49$	−0.376217	+	2.61665i	−0.0537453	+	0.373806i
$50$	0.909632	+	0.415415i	0.128641	+	0.0587486i
$51$	−0.677719	+	0.922790i	−0.0948997	+	0.129216i
$52$	0.434534	+	0.951496i	0.0602590	+	0.131949i
$53$	4.00210	+	4.61867i	0.549731	+	0.634424i	0.960820	−	0.277172i	$-0.0893970\pi$
$53$	4.00210	+	4.61867i	0.549731	+	0.634424i	−0.411089	+	0.911595i	$0.634852\pi$
$54$	−2.61436	−	4.49056i	−0.355769	−	0.611088i
$55$	−3.62905	−	1.06558i	−0.489341	−	0.143683i
$56$	1.36683	−	1.57741i	0.182651	−	0.210790i
$57$	−0.103557	−	1.28299i	−0.0137164	−	0.169936i
$58$	−6.03290	−	3.87711i	−0.792158	−	0.509089i
$59$	6.87698	+	5.95894i	0.895306	+	0.775787i	0.975271	−	0.221010i	$-0.0709354\pi$
$59$	6.87698	+	5.95894i	0.895306	+	0.775787i	−0.0799651	+	0.996798i	$0.525481\pi$
$60$	1.61724	−	0.620098i	0.208785	−	0.0800543i
$61$	11.8254	−	1.70023i	1.51408	−	0.217693i	0.665358	−	0.746524i	$-0.268279\pi$
$61$	11.8254	−	1.70023i	1.51408	−	0.217693i	0.848727	+	0.528832i	$0.177370\pi$
$62$	4.28068	−	3.70923i	0.543647	−	0.471073i
$63$	−1.00427	−	6.18057i	−0.126527	−	0.778679i
$64$	0.959493	−	0.281733i	0.119937	−	0.0352166i
$65$	−0.434534	+	0.951496i	−0.0538973	+	0.118019i
$66$	−5.72079	+	3.19201i	−0.704180	+	0.392910i
$67$	−1.86860	−	2.90760i	−0.228286	−	0.355219i	0.708148	−	0.706064i	$-0.249531\pi$
$67$	−1.86860	−	2.90760i	−0.228286	−	0.355219i	−0.936434	+	0.350845i	$0.885895\pi$
$68$	−0.661021			−0.0801605
$69$	−3.21735	−	7.65824i	−0.387324	−	0.921944i
$70$	2.08721			0.249469
$71$	5.63612	+	8.76998i	0.668885	+	1.04081i	0.995418	+	0.0956194i	$0.0304832\pi$
$71$	5.63612	+	8.76998i	0.668885	+	1.04081i	−0.326533	+	0.945186i	$0.605880\pi$
$72$	1.19615	−	2.75122i	0.140968	−	0.324235i
$73$	4.81545	−	10.5444i	0.563606	−	1.23412i	−0.386527	−	0.922278i	$-0.626325\pi$
$73$	4.81545	−	10.5444i	0.563606	−	1.23412i	0.950133	−	0.311846i	$-0.100947\pi$
$74$	3.53595	−	1.03825i	0.411046	−	0.120694i
$75$	1.52771	+	0.816154i	0.176405	+	0.0942413i
$76$	0.561631	−	0.486656i	0.0644235	−	0.0558233i
$77$	−7.81401	+	1.12348i	−0.890489	+	0.128033i
$78$	0.648637	+	1.69167i	0.0734436	+	0.191544i
$79$	4.94711	+	4.28670i	0.556594	+	0.482291i	0.887141	−	0.461498i	$-0.152688\pi$
$79$	4.94711	+	4.28670i	0.556594	+	0.482291i	−0.330548	+	0.943789i	$0.607233\pi$
$80$	0.841254	+	0.540641i	0.0940550	+	0.0604455i
$81$	−4.03550	−	8.04455i	−0.448388	−	0.893839i
$82$	−7.92562	+	9.14666i	−0.875239	+	1.01008i
$83$	−1.44461	−	0.424176i	−0.158567	−	0.0465594i	0.201486	−	0.979491i	$-0.435423\pi$
$83$	−1.44461	−	0.424176i	−0.158567	−	0.0465594i	−0.360052	+	0.932932i	$0.617241\pi$
$84$	2.53283	−	2.57956i	0.276354	−	0.281453i
$85$	−0.432877	−	0.499566i	−0.0469521	−	0.0541856i
$86$	2.63203	+	5.76333i	0.283819	+	0.621476i
$87$	−10.0112	−	7.35248i	−1.07332	−	0.788269i
$88$	−3.44046	−	1.57121i	−0.366754	−	0.167491i
$89$	−1.15319	+	8.02060i	−0.122238	+	0.850182i	0.832774	+	0.553613i	$0.186751\pi$
$89$	−1.15319	+	8.02060i	−0.122238	+	0.850182i	−0.955012	+	0.296568i	$0.904158\pi$
$90$	2.86255	−	0.897676i	0.301739	−	0.0946233i
$91$			2.18327i			0.228869i
$92$	2.46411	−	4.11438i	0.256901	−	0.428954i
$93$	7.79972	−	5.95081i	0.808793	−	0.617071i
$94$	2.23085	−	1.43368i	0.230094	−	0.147873i
$95$	0.735580	+	0.105760i	0.0754690	+	0.0108508i
$96$	1.68903	−	0.383629i	0.172386	−	0.0391539i
$97$	4.53637	+	15.4495i	0.460599	+	1.56866i	0.782981	+	0.622046i	$0.213698\pi$
$97$	4.53637	+	15.4495i	0.460599	+	1.56866i	−0.322382	+	0.946610i	$0.604484\pi$
$98$	−2.40466	+	1.09817i	−0.242907	+	0.110932i
$99$	−10.2335	+	4.90151i	−1.02850	+	0.492620i
$100$	0.142315	+	0.989821i	0.0142315	+	0.0989821i
$101$	−0.826971	+	2.81640i	−0.0822867	+	0.280243i	−0.990350	−	0.138591i	$-0.955743\pi$
$101$	−0.826971	+	2.81640i	−0.0822867	+	0.280243i	0.908063	+	0.418833i	$0.137561\pi$
$102$	−1.14270	−	0.0712359i	−0.113144	−	0.00705340i
$103$	1.09847	−	1.70926i	0.108236	−	0.168418i	−0.782910	−	0.622135i	$-0.786266\pi$
$103$	1.09847	−	1.70926i	0.108236	−	0.168418i	0.891146	+	0.453716i	$0.149902\pi$
$104$	−0.565523	+	0.879970i	−0.0554541	+	0.0862882i
$105$	3.60815	+	0.224931i	0.352119	+	0.0219510i
$106$	−1.72177	+	5.86383i	−0.167234	+	0.569545i
$107$	−1.01467	−	7.05718i	−0.0980917	−	0.682243i	−0.978230	−	0.207525i	$-0.933459\pi$
$107$	−1.01467	−	7.05718i	−0.0980917	−	0.682243i	0.880138	−	0.474718i	$-0.157450\pi$
$108$	2.36427	−	4.62712i	0.227502	−	0.445245i
$109$	−3.21687	+	1.46910i	−0.308120	+	0.140714i	−0.563474	−	0.826134i	$-0.690535\pi$
$109$	−3.21687	+	1.46910i	−0.308120	+	0.140714i	0.255353	+	0.966848i	$0.417808\pi$
$110$	−1.06558	−	3.62905i	−0.101599	−	0.346016i
$111$	6.22447	−	1.41376i	0.590800	−	0.134188i
$112$	2.06597	+	0.297041i	0.195215	+	0.0280677i
$113$	7.64121	−	4.91071i	0.718824	−	0.461960i	−0.129403	−	0.991592i	$-0.541306\pi$
$113$	7.64121	−	4.91071i	0.718824	−	0.461960i	0.848228	+	0.529632i	$0.177670\pi$
$114$	1.02333	−	0.780755i	0.0958440	−	0.0731244i
$115$	4.72309	−	0.832098i	0.440431	−	0.0775935i
$116$		−	7.17132i		−	0.665840i
$117$	0.938989	+	2.99429i	0.0868096	+	0.276822i
$118$	−1.29500	+	9.00693i	−0.119214	+	0.829155i
$119$	−1.25501	−	0.573144i	−0.115047	−	0.0525400i
$120$	1.39601	+	1.02526i	0.127437	+	0.0935932i
$121$	1.37314	+	3.00675i	0.124831	+	0.273341i
$122$	7.82361	+	9.02893i	0.708316	+	0.817441i
$123$	−14.6867	+	14.9577i	−1.32425	+	1.34869i
$124$	5.43471	+	1.59578i	0.488052	+	0.143305i
$125$	−0.654861	+	0.755750i	−0.0585725	+	0.0675963i
$126$	4.65648	−	4.18632i	0.414832	−	0.372947i
$127$	−9.09044	−	5.84207i	−0.806646	−	0.518400i	0.0711320	−	0.997467i	$-0.477339\pi$
$127$	−9.09044	−	5.84207i	−0.806646	−	0.518400i	−0.877779	+	0.479067i	$0.840975\pi$
$128$	0.755750	+	0.654861i	0.0667995	+	0.0578821i
$129$	3.92888	+	10.2467i	0.345918	+	0.902171i
$130$	−1.03538	+	0.148865i	−0.0908085	+	0.0130563i
$131$	7.67770	−	6.65277i	0.670804	−	0.581255i	−0.251436	−	0.967874i	$-0.580903\pi$
$131$	7.67770	−	6.65277i	0.670804	−	0.581255i	0.922239	+	0.386619i	$0.126357\pi$
$132$	−5.77818	−	3.08690i	−0.502926	−	0.268680i
$133$	1.48827	−	0.436995i	0.129049	−	0.0378923i
$134$	1.43579	−	3.14393i	0.124033	−	0.271594i
$135$	5.04521	−	1.24332i	0.434223	−	0.107008i
$136$	−0.357375	−	0.556086i	−0.0306446	−	0.0476840i
$137$	4.02457			0.343843			0.171921	−	0.985111i	$-0.445003\pi$
$137$	4.02457			0.343843			0.171921	+	0.985111i	$0.445003\pi$
$138$	4.70309	−	6.84697i	0.400354	−	0.582853i
$139$	−10.2689			−0.870997			−0.435499	−	0.900189i	$-0.643428\pi$
$139$	−10.2689			−0.870997			−0.435499	+	0.900189i	$0.643428\pi$
$140$	1.12843	+	1.75587i	0.0953698	+	0.148398i
$141$	4.01096	−	2.23798i	0.337784	−	0.188472i
$142$	−4.33066	+	9.48282i	−0.363421	+	0.795780i
$143$	3.79607	−	1.11463i	0.317443	−	0.0932097i
$144$	2.96116	−	0.481156i	0.246764	−	0.0400963i
$145$	5.41972	−	4.69621i	0.450083	−	0.389999i
$146$	11.4739	−	1.64970i	0.949587	−	0.136530i
$147$	−4.27527	+	1.63926i	−0.352618	+	0.135204i
$148$	2.78511	+	2.41331i	0.228935	+	0.198373i
$149$	3.89009	+	2.50001i	0.318689	+	0.204809i	0.690198	−	0.723620i	$-0.257523\pi$
$149$	3.89009	+	2.50001i	0.318689	+	0.204809i	−0.371510	+	0.928429i	$0.621160\pi$
$150$	0.139349	+	1.72644i	0.0113778	+	0.140963i
$151$	1.80242	−	2.08010i	0.146679	−	0.169276i	−0.677656	−	0.735379i	$-0.737004\pi$
$151$	1.80242	−	2.08010i	0.146679	−	0.169276i	0.824335	+	0.566103i	$0.191550\pi$
$152$	0.713042	+	0.209368i	0.0578353	+	0.0169820i
$153$	−1.96771	−	0.246290i	−0.159080	−	0.0199114i
$154$	−5.16971	−	5.96616i	−0.416587	−	0.480767i
$155$	2.35297	+	5.15229i	0.188995	+	0.413842i
$156$	−1.07245	+	1.46026i	−0.0858645	+	0.116914i
$157$	3.60648	+	1.64702i	0.287829	+	0.131447i	0.554097	−	0.832452i	$-0.313064\pi$
$157$	3.60648	+	1.64702i	0.287829	+	0.131447i	−0.266269	+	0.963899i	$0.585791\pi$
$158$	−0.931588	+	6.47934i	−0.0741132	+	0.515469i
$159$	−3.60835	+	9.95122i	−0.286161	+	0.789183i
$160$			1.00000i			0.0790569i
$161$	8.24576	−	5.67501i	0.649857	−	0.447254i
$162$	4.58575	−	7.74409i	0.360291	−	0.608433i
$163$	1.93503	−	1.24357i	0.151563	−	0.0974037i	−0.462661	−	0.886535i	$-0.653105\pi$
$163$	1.93503	−	1.24357i	0.151563	−	0.0974037i	0.614224	+	0.789131i	$0.289469\pi$
$164$	−11.9796	−	1.72240i	−0.935447	−	0.134497i
$165$	−1.45098	−	6.38835i	−0.112959	−	0.497332i
$166$	−0.424176	−	1.44461i	−0.0329225	−	0.112124i
$167$	−17.6967	+	8.08182i	−1.36941	+	0.625390i	−0.958187	−	0.286143i	$-0.907627\pi$
$167$	−17.6967	+	8.08182i	−1.36941	+	0.625390i	−0.411227	+	0.911533i	$0.634900\pi$
$168$	3.53941	+	0.736135i	0.273072	+	0.0567941i
$169$	1.69438	+	11.7847i	0.130337	+	0.906512i
$170$	0.186231	−	0.634245i	0.0142833	−	0.0486444i
$171$	1.85317	−	1.23941i	0.141716	−	0.0947798i
$172$	−3.42544	+	5.33009i	−0.261188	+	0.406416i
$173$	8.05290	−	12.5305i	0.612250	−	0.952680i	−0.387278	−	0.921963i	$-0.626585\pi$
$173$	8.05290	−	12.5305i	0.612250	−	0.952680i	0.999528	−	0.0307170i	$-0.00977906\pi$
$174$	0.772828	−	12.3970i	0.0585879	−	0.939816i
$175$	−0.588035	+	2.00266i	−0.0444513	+	0.151387i
$176$	−0.538271	−	3.74376i	−0.0405737	−	0.282196i
$177$	−3.20931	+	15.4307i	−0.241226	+	1.15984i
$178$	−7.37082	+	3.36614i	−0.552466	+	0.252303i
$179$	−5.78159	−	19.6903i	−0.432136	−	1.47172i	−0.831809	−	0.555062i	$-0.812694\pi$
$179$	−5.78159	−	19.6903i	−0.432136	−	1.47172i	0.399673	−	0.916658i	$-0.369124\pi$
$180$	2.30278	+	1.92281i	0.171639	+	0.143318i
$181$	23.9345	+	3.44127i	1.77904	+	0.255787i	0.951944	−	0.306274i	$-0.0990823\pi$
$181$	23.9345	+	3.44127i	1.77904	+	0.255787i	0.827096	+	0.562061i	$0.189991\pi$
$182$	−1.83668	+	1.18036i	−0.136144	+	0.0874945i
$183$	12.5516	+	16.4514i	0.927843	+	1.21612i
$184$	4.79344	−	0.151462i	0.353377	−	0.0111659i
$185$			3.68523i			0.270943i
$186$	9.22299	+	3.34429i	0.676263	+	0.245215i
$187$	−0.355808	+	2.47470i	−0.0260193	+	0.180968i
$188$	2.41217	+	1.10160i	0.175926	+	0.0803427i
$189$	8.50077	−	6.73505i	0.618340	−	0.489903i
$190$	0.308713	+	0.675988i	0.0223964	+	0.0490413i
$191$	4.73421	+	5.46356i	0.342555	+	0.395330i	0.900720	−	0.434401i	$-0.143040\pi$
$191$	4.73421	+	5.46356i	0.342555	+	0.395330i	−0.558165	+	0.829730i	$0.688494\pi$
$192$	1.23589	+	1.21350i	0.0891926	+	0.0875767i
$193$	−23.1077	−	6.78503i	−1.66333	−	0.488397i	−0.691163	−	0.722698i	$-0.742902\pi$
$193$	−23.1077	−	6.78503i	−1.66333	−	0.488397i	−0.972164	+	0.234301i	$0.924720\pi$
$194$	−10.5444	+	12.1688i	−0.757041	+	0.873672i
$195$	−1.80589	+	0.145763i	−0.129323	+	0.0104383i
$196$	−2.22390	−	1.42921i	−0.158850	−	0.102087i
$197$	−8.50246	−	7.36742i	−0.605775	−	0.524907i	0.297080	−	0.954853i	$-0.403987\pi$
$197$	−8.50246	−	7.36742i	−0.605775	−	0.524907i	−0.902855	+	0.429946i	$0.858533\pi$
$198$	−9.65605	−	5.95901i	−0.686226	−	0.423488i
$199$	−1.92141	+	0.276256i	−0.136205	+	0.0195833i	−0.210080	−	0.977684i	$-0.567372\pi$
$199$	−1.92141	+	0.276256i	−0.136205	+	0.0195833i	0.0738752	+	0.997267i	$0.476463\pi$
$200$	−0.755750	+	0.654861i	−0.0534396	+	0.0463056i
$201$	2.82085	−	5.28017i	0.198967	−	0.372434i
$202$	−2.81640	+	0.826971i	−0.198161	+	0.0581855i
$203$	6.21795	−	13.6154i	0.436415	−	0.955615i
$204$	−0.557865	−	0.999816i	−0.0390583	−	0.0700011i
$205$	−6.54325	−	10.1815i	−0.457000	−	0.711106i
$206$	2.03180			0.141562
$207$	8.86808	−	11.3295i	0.616374	−	0.787453i
$208$	−1.04602			−0.0725286
$209$	−1.51961	−	2.36456i	−0.105114	−	0.163560i
$210$	1.76149	+	3.15698i	0.121554	+	0.217852i
$211$	0.862032	−	1.88759i	0.0593448	−	0.129947i	−0.877636	−	0.479327i	$-0.840881\pi$
$211$	0.862032	−	1.88759i	0.0593448	−	0.129947i	0.936981	+	0.349380i	$0.113608\pi$
$212$	−5.86383	+	1.72177i	−0.402729	+	0.118252i
$213$	−8.50832	+	15.9262i	−0.582980	+	1.09125i
$214$	5.38830	−	4.66899i	0.368337	−	0.319166i
$215$	−6.27140	+	0.901692i	−0.427706	+	0.0614949i
$216$	5.17080	−	0.512657i	0.351828	−	0.0348819i
$217$	8.93468	+	7.74194i	0.606526	+	0.525557i
$218$	−2.97505	−	1.91195i	−0.201496	−	0.129494i
$219$	20.0127	−	1.61532i	1.35233	−	0.109153i
$220$	2.47685	−	2.85844i	0.166989	−	0.192716i
$221$	0.663435	+	0.194802i	0.0446274	+	0.0131038i
$222$	4.55453	+	4.47202i	0.305680	+	0.300142i
$223$	−5.89769	−	6.80630i	−0.394939	−	0.455784i	0.523102	−	0.852270i	$-0.324775\pi$
$223$	−5.89769	−	6.80630i	−0.394939	−	0.455784i	−0.918041	+	0.396487i	$0.870229\pi$
$224$	0.867059	+	1.89859i	0.0579328	+	0.126855i
$225$	0.0548407	+	2.99950i	0.00365605	+	0.199967i
$226$	8.26230	+	3.77327i	0.549600	+	0.250994i
$227$	−2.43304	+	16.9222i	−0.161487	+	1.12317i	0.734346	+	0.678775i	$0.237489\pi$
$227$	−2.43304	+	16.9222i	−0.161487	+	1.12317i	−0.895833	+	0.444390i	$0.853420\pi$
$228$	1.21007	+	0.438775i	0.0801388	+	0.0290586i
$229$		−	12.0696i		−	0.797582i	−0.917042	−	0.398791i	$-0.869430\pi$
$229$		−	12.0696i		−	0.797582i	0.917042	−	0.398791i	$-0.130570\pi$
$230$	3.25350	+	3.52345i	0.214530	+	0.232330i
$231$	−8.29390	−	10.8708i	−0.545698	−	0.715246i
$232$	6.03290	−	3.87711i	0.396079	−	0.254545i
$233$	20.3546	+	2.92655i	1.33347	+	0.191725i	0.771923	−	0.635717i	$-0.219295\pi$
$233$	20.3546	+	2.92655i	1.33347	+	0.191725i	0.561552	+	0.827441i	$0.310204\pi$
$234$	−2.01130	+	2.40876i	−0.131483	+	0.157466i
$235$	0.747102	+	2.54440i	0.0487356	+	0.165978i
$236$	−8.27724	+	3.78009i	−0.538802	+	0.246063i
$237$	−2.30869	+	11.1004i	−0.149965	+	0.721049i
$238$	−0.196350	−	1.36565i	−0.0127275	−	0.0885217i
$239$	1.90983	−	6.50428i	0.123537	−	0.420727i	−0.874380	−	0.485241i	$-0.838732\pi$
$239$	1.90983	−	6.50428i	0.123537	−	0.420727i	0.997917	+	0.0645146i	$0.0205499\pi$
$240$	−0.107766	+	1.72869i	−0.00695629	+	0.111587i
$241$	16.3601	−	25.4568i	1.05385	−	1.63982i	0.338626	−	0.940921i	$-0.390038\pi$
$241$	16.3601	−	25.4568i	1.05385	−	1.63982i	0.715221	−	0.698898i	$-0.246326\pi$
$242$	−1.78706	+	2.78073i	−0.114877	+	0.178752i
$243$	8.76192	−	12.8930i	0.562077	−	0.827085i
$244$	−3.36585	+	11.4630i	−0.215477	+	0.733846i
$245$	−0.376217	−	2.61665i	−0.0240356	−	0.167171i
$246$	−20.5234	−	4.26850i	−1.30852	−	0.272150i
$247$	−0.707099	+	0.322921i	−0.0449916	+	0.0205470i
$248$	1.59578	+	5.43471i	0.101332	+	0.345105i
$249$	−0.577591	−	2.54301i	−0.0366033	−	0.161156i
$250$	−0.989821	−	0.142315i	−0.0626018	−	0.00900078i
$251$	−12.1385	+	7.80094i	−0.766176	+	0.492391i	−0.864420	−	0.502771i	$-0.832314\pi$
$251$	−12.1385	+	7.80094i	−0.766176	+	0.492391i	0.0982440	+	0.995162i	$0.468677\pi$
$252$	6.03924	+	1.65398i	0.380436	+	0.104191i
$253$	−14.0769	−	11.4397i	−0.885007	−	0.719207i
$254$		−	10.8058i		−	0.678018i
$255$	0.390287	−	1.07635i	0.0244407	−	0.0674034i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	10.7202	+	4.89577i	0.668710	+	0.305390i	0.720689	−	0.693258i	$-0.243826\pi$
$257$	10.7202	+	4.89577i	0.668710	+	0.305390i	−0.0519788	+	0.998648i	$0.516553\pi$
$258$	−6.49595	+	8.84496i	−0.404420	+	0.550663i
$259$	3.19531	+	6.99675i	0.198547	+	0.434757i
$260$	−0.684999	−	0.790531i	−0.0424819	−	0.0490267i
$261$	2.67197	−	21.3474i	0.165391	−	1.32137i
$262$	9.74754	+	2.86214i	0.602205	+	0.176823i
$263$	11.5553	−	13.3355i	0.712528	−	0.822301i	−0.277859	−	0.960622i	$-0.589625\pi$
$263$	11.5553	−	13.3355i	0.712528	−	0.822301i	0.990388	+	0.138320i	$0.0441704\pi$
$264$	−0.527055	−	6.52982i	−0.0324380	−	0.401883i
$265$	−5.14122	−	3.30406i	−0.315823	−	0.202967i
$266$	1.17224	+	1.01575i	0.0718748	+	0.0622799i
$267$	−13.1047	+	5.02470i	−0.801992	+	0.307507i
$268$	3.42109	−	0.491878i	0.208976	−	0.0300462i
$269$	12.4490	−	10.7872i	0.759032	−	0.657705i	−0.186787	−	0.982400i	$-0.559807\pi$
$269$	12.4490	−	10.7872i	0.759032	−	0.657705i	0.945819	+	0.324696i	$0.105262\pi$
$270$	3.77360	+	3.57211i	0.229654	+	0.217392i
$271$	−7.61968	+	2.23734i	−0.462863	+	0.135909i	−0.504846	−	0.863210i	$-0.668451\pi$
$271$	−7.61968	+	2.23734i	−0.462863	+	0.135909i	0.0419830	+	0.999118i	$0.486632\pi$
$272$	0.274598	−	0.601286i	0.0166499	−	0.0364583i
$273$	−3.30227	+	1.84256i	−0.199862	+	0.111517i
$274$	2.17585	+	3.38569i	0.131448	+	0.204537i
$275$	3.78226			0.228079
$276$	8.30272	+	0.254741i	0.499765	+	0.0153336i
$277$	−27.5752			−1.65683			−0.828416	−	0.560113i	$-0.810758\pi$
$277$	−27.5752			−1.65683			−0.828416	+	0.560113i	$0.810758\pi$
$278$	−5.55179	−	8.63875i	−0.332974	−	0.518118i
$279$	15.5833	+	6.77519i	0.932950	+	0.405620i
$280$	−0.867059	+	1.89859i	−0.0518167	+	0.113463i
$281$	0.389715	−	0.114431i	0.0232484	−	0.00682636i	−0.270088	−	0.962836i	$-0.587053\pi$
$281$	0.389715	−	0.114431i	0.0232484	−	0.00682636i	0.293336	+	0.956009i	$0.405235\pi$
$282$	4.05120	+	2.16429i	0.241245	+	0.128881i
$283$	−15.6551	+	13.5652i	−0.930598	+	0.806368i	−0.981328	−	0.192344i	$-0.938391\pi$
$283$	−15.6551	+	13.5652i	−0.930598	+	0.806368i	0.0507290	+	0.998712i	$0.483846\pi$
$284$	−10.3188	+	1.48362i	−0.612307	+	0.0880365i
$285$	0.460822	+	1.20185i	0.0272968	+	0.0711912i
$286$	2.98999	+	2.59084i	0.176802	+	0.153200i
$287$	−21.2509	−	13.6571i	−1.25440	−	0.806155i
$288$	2.00570	+	2.23096i	0.118187	+	0.131460i
$289$	10.8465	−	12.5175i	0.638029	−	0.736325i
$290$	6.88083	+	2.02039i	0.404056	+	0.118642i
$291$	−19.5394	+	19.8999i	−1.14542	+	1.16655i
$292$	7.59108	+	8.76057i	0.444234	+	0.512674i
$293$	9.23610	+	20.2242i	0.539579	+	1.18151i	0.961481	+	0.274871i	$0.0886351\pi$
$293$	9.23610	+	20.2242i	0.539579	+	1.18151i	−0.421903	+	0.906641i	$0.638638\pi$
$294$	−3.69042	−	2.71033i	−0.215230	−	0.158070i
$295$	−8.27724	−	3.78009i	−0.481919	−	0.220085i
$296$	−0.524462	+	3.64772i	−0.0304838	+	0.212019i
$297$	−16.0502	−	11.3419i	−0.931326	−	0.658124i
$298$			4.62416i			0.267870i
$299$	−3.68561	+	3.40324i	−0.213144	+	0.196814i
$300$	−1.37703	+	1.05061i	−0.0795030	+	0.0606570i
$301$	−11.1250	+	7.14962i	−0.641236	+	0.412097i
$302$	2.72435	+	0.391703i	0.156769	+	0.0225400i
$303$	−4.95782	+	1.12607i	−0.284819	+	0.0646908i
$304$	0.209368	+	0.713042i	0.0120081	+	0.0408958i
$305$	−10.8674	+	4.96296i	−0.622263	+	0.284178i
$306$	−0.856631	−	1.78850i	−0.0489703	−	0.102242i
$307$	0.868901	+	6.04334i	0.0495908	+	0.344912i	0.999478	+	0.0323177i	$0.0102888\pi$
$307$	0.868901	+	6.04334i	0.0495908	+	0.344912i	−0.949887	+	0.312594i	$0.898802\pi$
$308$	2.22410	−	7.57459i	0.126730	−	0.431602i
$309$	3.51236	+	0.218960i	0.199811	+	0.0124562i
$310$	−3.06227	+	4.76499i	−0.173925	+	0.270633i
$311$	−7.09806	+	11.0448i	−0.402494	+	0.626293i	−0.982046	−	0.188643i	$-0.939591\pi$
$311$	−7.09806	+	11.0448i	−0.402494	+	0.626293i	0.579552	+	0.814935i	$0.303228\pi$
$312$	−1.80825	−	0.112726i	−0.102372	−	0.00638186i
$313$	−2.44364	+	8.32229i	−0.138123	+	0.470404i	−0.999280	−	0.0379351i	$-0.987922\pi$
$313$	−2.44364	+	8.32229i	−0.138123	+	0.470404i	0.861157	+	0.508339i	$0.169740\pi$
$314$	0.564246	+	3.92441i	0.0318422	+	0.221467i
$315$	2.70486	+	5.64728i	0.152402	+	0.318188i
$316$	−5.95442	+	2.71929i	−0.334962	+	0.152972i
$317$	−8.55649	−	29.1407i	−0.480580	−	1.63671i	−0.741214	−	0.671269i	$-0.765750\pi$
$317$	−8.55649	−	29.1407i	−0.480580	−	1.63671i	0.260634	−	0.965438i	$-0.416069\pi$
$318$	−10.3223	+	2.34450i	−0.578847	+	0.131473i
$319$	−26.8477	−	3.86011i	−1.50318	−	0.216125i
$320$	−0.841254	+	0.540641i	−0.0470275	+	0.0302227i
$321$	9.81789	−	7.49058i	0.547981	−	0.418084i
$322$	9.23212	+	3.86863i	0.514486	+	0.215590i
$323$		−	0.491234i		−	0.0273330i
$324$	8.99398	−	0.328989i	0.499666	−	0.0182772i
$325$	0.148865	−	1.03538i	0.00825752	−	0.0574323i
$326$	2.09231	+	0.955526i	0.115882	+	0.0529217i
$327$	−4.93692	−	3.62579i	−0.273012	−	0.200507i
$328$	−5.02767	−	11.0091i	−0.277607	−	0.607874i
$329$	3.62458	+	4.18299i	0.199830	+	0.230616i
$330$	4.58976	−	4.67445i	0.252658	−	0.257320i
$331$	−0.868148	−	0.254911i	−0.0477177	−	0.0140112i	0.257787	−	0.966202i	$-0.417007\pi$
$331$	−0.868148	−	0.254911i	−0.0477177	−	0.0140112i	−0.305504	+	0.952191i	$0.598825\pi$
$332$	0.985958	−	1.13786i	0.0541115	−	0.0624480i
$333$	7.39146	+	8.22158i	0.405049	+	0.450540i
$334$	−16.3664	−	10.5181i	−0.895531	−	0.575523i
$335$	2.61207	+	2.26337i	0.142713	+	0.123661i
$336$	1.29428	+	3.37553i	0.0706085	+	0.184150i
$337$	26.5750	−	3.82090i	1.44763	−	0.208138i	0.626742	−	0.779227i	$-0.284388\pi$
$337$	26.5750	−	3.82090i	1.44763	−	0.208138i	0.820888	+	0.571089i	$0.193479\pi$
$338$	−8.99783	+	7.79666i	−0.489417	+	0.424083i
$339$	13.8764	+	7.41322i	0.753661	+	0.402631i
$340$	0.634245	−	0.186231i	0.0343968	−	0.0100998i
$341$	8.89955	−	19.4873i	0.481937	−	1.05530i
$342$	2.04456	+	0.888914i	0.110557	+	0.0480669i
$343$	−10.8821	−	16.9329i	−0.587577	−	0.914288i
$344$	−6.33590			−0.341609
$345$	5.24460	+	6.44159i	0.282360	+	0.346804i
$346$	14.8951			0.800765
$347$	2.61529	+	4.06947i	0.140396	+	0.218461i	0.904330	−	0.426834i	$-0.140371\pi$
$347$	2.61529	+	4.06947i	0.140396	+	0.218461i	−0.763934	+	0.645295i	$0.776735\pi$
$348$	10.8469	−	6.05219i	0.581453	−	0.324432i
$349$	−8.19723	+	17.9494i	−0.438788	+	0.960811i	0.553031	+	0.833160i	$0.313471\pi$
$349$	−8.19723	+	17.9494i	−0.438788	+	0.960811i	−0.991819	+	0.127651i	$0.959256\pi$
$350$	−2.00266	+	0.588035i	−0.107047	+	0.0314318i
$351$	−3.73651	+	3.94727i	−0.199440	+	0.210690i
$352$	2.85844	−	2.47685i	0.152355	−	0.132017i
$353$	−31.6214	+	4.54647i	−1.68304	+	0.241984i	−0.916448	−	0.400155i	$-0.868956\pi$
$353$	−31.6214	+	4.54647i	−1.68304	+	0.241984i	−0.766589	+	0.642139i	$0.778047\pi$
$354$	−14.7162	+	5.64261i	−0.782157	+	0.299901i
$355$	−7.87861	−	6.82685i	−0.418153	−	0.362332i
$356$	−6.81674	−	4.38085i	−0.361287	−	0.232185i
$357$	−0.192259	−	2.38195i	−0.0101754	−	0.126066i
$358$	13.4388	−	15.5091i	0.710260	−	0.819684i
$359$	3.05208	+	0.896172i	0.161083	+	0.0472981i	0.361280	−	0.932458i	$-0.382340\pi$
$359$	3.05208	+	0.896172i	0.161083	+	0.0472981i	−0.200197	+	0.979756i	$0.564158\pi$
$360$	−0.372591	+	2.97677i	−0.0196373	+	0.156890i
$361$	−12.0807	−	13.9419i	−0.635826	−	0.733783i
$362$	10.0450	+	21.9955i	0.527954	+	1.15606i
$363$	−3.38896	+	4.61444i	−0.177874	+	0.242195i
$364$	−1.98597	−	0.906963i	−0.104093	−	0.0475378i
$365$	−1.64970	+	11.4739i	−0.0863492	+	0.600572i
$366$	−7.05387	+	19.4534i	−0.368712	+	1.01684i
$367$		−	29.8589i		−	1.55862i	−0.626637	−	0.779311i	$-0.715569\pi$
$367$		−	29.8589i		−	1.55862i	0.626637	−	0.779311i	$-0.284431\pi$
$368$	2.71895	+	3.95061i	0.141735	+	0.205940i
$369$	−35.0187	−	9.59068i	−1.82300	−	0.499271i
$370$	−3.10021	+	1.99238i	−0.161172	+	0.103579i
$371$	−12.6259	−	1.81533i	−0.655504	−	0.0942473i
$372$	2.17293	+	9.56693i	0.112661	+	0.496022i
$373$	10.3528	+	35.2584i	0.536047	+	1.82561i	0.563682	+	0.825992i	$0.309384\pi$
$373$	10.3528	+	35.2584i	0.536047	+	1.82561i	−0.0276350	+	0.999618i	$0.508798\pi$
$374$	−2.27422	+	1.03860i	−0.117597	+	0.0537047i
$375$	−1.69576	−	0.352688i	−0.0875688	−	0.0182128i
$376$	0.377393	+	2.62482i	0.0194625	+	0.135365i
$377$	−2.11338	+	7.19750i	−0.108845	+	0.370690i
$378$	10.2618	+	3.51006i	0.527808	+	0.180538i
$379$	3.42098	−	5.32315i	0.175724	−	0.273432i	−0.742208	−	0.670170i	$-0.766221\pi$
$379$	3.42098	−	5.32315i	0.175724	−	0.273432i	0.917932	+	0.396738i	$0.129858\pi$
$380$	−0.401774	+	0.625173i	−0.0206106	+	0.0320707i
$381$	1.16451	−	18.6800i	0.0596595	−	0.957005i
$382$	−2.03674	+	6.93649i	−0.104209	+	0.354902i
$383$	1.05071	+	7.30787i	0.0536889	+	0.373415i	0.998897	+	0.0469473i	$0.0149493\pi$
$383$	1.05071	+	7.30787i	0.0536889	+	0.373415i	−0.945208	+	0.326468i	$0.894142\pi$
$384$	−0.352688	+	1.69576i	−0.0179981	+	0.0865365i
$385$	7.18096	−	3.27944i	0.365976	−	0.167136i
$386$	−6.78503	−	23.1077i	−0.345349	−	1.17615i
$387$	−12.1827	+	14.5902i	−0.619282	+	0.741661i
$388$	−15.9378	−	2.29151i	−0.809119	−	0.116334i
$389$	−12.8737	+	8.27346i	−0.652725	+	0.419481i	−0.824661	−	0.565627i	$-0.808634\pi$
$389$	−12.8737	+	8.27346i	−0.652725	+	0.419481i	0.171936	+	0.985108i	$0.444998\pi$
$390$	−1.09896	−	1.44041i	−0.0556481	−	0.0729379i
$391$	−0.988751	−	3.01201i	−0.0500033	−	0.152324i
$392$		−	2.64355i		−	0.133520i
$393$	16.5421	+	5.99822i	0.834438	+	0.302570i
$394$	1.60109	−	11.1359i	0.0806620	−	0.561016i
$395$	−5.95442	−	2.71929i	−0.299599	−	0.136822i
$396$	−0.207422	−	11.3449i	−0.0104233	−	0.570101i
$397$	−0.579325	−	1.26854i	−0.0290755	−	0.0636664i	0.894537	−	0.446994i	$-0.147505\pi$
$397$	−0.579325	−	1.26854i	−0.0290755	−	0.0636664i	−0.923613	+	0.383327i	$0.874778\pi$
$398$	−1.27119	−	1.46703i	−0.0637191	−	0.0735357i
$399$	1.91699	+	1.88226i	0.0959693	+	0.0942307i
$400$	−0.959493	−	0.281733i	−0.0479746	−	0.0140866i
$401$	7.67746	−	8.86026i	0.383394	−	0.442460i	−0.530947	−	0.847405i	$-0.678164\pi$
$401$	7.67746	−	8.86026i	0.383394	−	0.442460i	0.914341	+	0.404945i	$0.132709\pi$
$402$	5.96702	−	0.481629i	0.297608	−	0.0240215i
$403$	−4.98429	−	3.20321i	−0.248285	−	0.159563i
$404$	−2.21835	−	1.92222i	−0.110367	−	0.0956338i
$405$	6.13844	+	6.58176i	0.305022	+	0.327050i
$406$	14.8157	−	2.13018i	0.735291	−	0.105719i
$407$	10.5340	−	9.12776i	0.522151	−	0.452446i
$408$	0.539495	−	1.00985i	0.0267090	−	0.0499949i
$409$	30.8241	−	9.05077i	1.52415	−	0.447532i	0.590898	−	0.806746i	$-0.298774\pi$
$409$	30.8241	−	9.05077i	1.52415	−	0.447532i	0.933255	+	0.359214i	$0.116955\pi$
$410$	5.02767	−	11.0091i	0.248299	−	0.543699i
$411$	3.39652	+	6.08730i	0.167538	+	0.300265i
$412$	1.09847	+	1.70926i	0.0541179	+	0.0842092i
$413$	−18.9927			−0.934568
$414$	14.3254	+	1.33512i	0.704056	+	0.0656177i
$415$	1.50560			0.0739070
$416$	−0.565523	−	0.879970i	−0.0277270	−	0.0431441i
$417$	−8.66638	−	15.5321i	−0.424395	−	0.760609i
$418$	1.16763	−	2.55676i	0.0571108	−	0.125055i
$419$	−21.0467	+	6.17988i	−1.02820	+	0.301907i	−0.751979	−	0.659187i	$-0.770900\pi$
$419$	−21.0467	+	6.17988i	−1.02820	+	0.301907i	−0.276221	+	0.961094i	$0.589082\pi$
$420$	−1.70348	+	3.18865i	−0.0831215	+	0.155590i
$421$	14.7437	−	12.7755i	0.718563	−	0.622638i	−0.216846	−	0.976206i	$-0.569577\pi$
$421$	14.7437	−	12.7755i	0.718563	−	0.622638i	0.935409	+	0.353568i	$0.115032\pi$
$422$	2.05399	−	0.295319i	0.0999867	−	0.0143759i
$423$	6.77005	+	4.17798i	0.329171	+	0.203140i
$424$	−4.61867	−	4.00210i	−0.224303	−	0.194359i
$425$	0.556086	+	0.357375i	0.0269741	+	0.0173352i
$426$	−17.9979	+	1.45270i	−0.872002	+	0.0703837i
$427$	−16.3295	+	18.8453i	−0.790241	+	0.911987i
$428$	6.84094	+	2.00868i	0.330669	+	0.0970933i
$429$	4.88958	+	4.80100i	0.236071	+	0.231794i
$430$	−4.14913	−	4.78835i	−0.200089	−	0.230915i
$431$	−6.91079	−	15.1325i	−0.332881	−	0.728907i	0.666989	−	0.745068i	$-0.267583\pi$
$431$	−6.91079	−	15.1325i	−0.332881	−	0.728907i	−0.999869	+	0.0161606i	$0.994856\pi$
$432$	3.22682	+	4.07279i	0.155250	+	0.195952i
$433$	−25.9047	−	11.8303i	−1.24490	−	0.568527i	−0.319525	−	0.947578i	$-0.603523\pi$
$433$	−25.9047	−	11.8303i	−1.24490	−	0.568527i	−0.925376	+	0.379051i	$0.876251\pi$
$434$	−1.68249	+	11.7019i	−0.0807619	+	0.561711i
$435$	11.6771	+	4.23417i	0.559875	+	0.203013i
$436$		−	3.53645i		−	0.169365i
$437$	3.05758	+	1.83119i	0.146264	+	0.0875977i
$438$	12.1786	+	15.9624i	0.581914	+	0.762714i
$439$	−2.76299	+	1.77567i	−0.131870	+	0.0847479i	−0.604913	−	0.796292i	$-0.706792\pi$
$439$	−2.76299	+	1.77567i	−0.131870	+	0.0847479i	0.473043	+	0.881040i	$0.343156\pi$
$440$	3.74376	+	0.538271i	0.178477	+	0.0256611i
$441$	−6.08753	−	5.08305i	−0.289882	−	0.242050i
$442$	0.194802	+	0.663435i	0.00926578	+	0.0315564i
$443$	−34.1311	+	15.5871i	−1.62162	+	0.740567i	−0.999115	−	0.0420525i	$-0.986610\pi$
$443$	−34.1311	+	15.5871i	−1.62162	+	0.740567i	−0.622500	+	0.782620i	$0.713883\pi$
$444$	−1.29974	+	6.24927i	−0.0616828	+	0.296577i
$445$	−1.15319	−	8.02060i	−0.0546664	−	0.380213i
$446$	2.53729	−	8.64122i	0.120144	−	0.409174i
$447$	−0.498329	+	7.99376i	−0.0235702	+	0.378092i
$448$	−1.12843	+	1.75587i	−0.0533134	+	0.0829572i
$449$	15.5718	−	24.2302i	0.734880	−	1.14349i	−0.249660	−	0.968334i	$-0.580319\pi$
$449$	15.5718	−	24.2302i	0.734880	−	1.14349i	0.984540	−	0.175161i	$-0.0560447\pi$
$450$	−2.49369	+	1.66779i	−0.117554	+	0.0786202i
$451$	−12.8965	+	43.9215i	−0.607273	+	2.06818i
$452$	1.29266	+	8.99067i	0.0608018	+	0.422886i
$453$	4.66737	+	0.970729i	0.219292	+	0.0456088i
$454$	−15.5513	+	7.10202i	−0.729857	+	0.333314i
$455$	−0.615098	−	2.09483i	−0.0288362	−	0.0982072i
$456$	0.285091	+	1.25519i	0.0133506	+	0.0587799i
$457$	16.3187	+	2.34628i	0.763357	+	0.109754i	0.512987	−	0.858396i	$-0.328539\pi$
$457$	16.3187	+	2.34628i	0.763357	+	0.109754i	0.250370	+	0.968150i	$0.419448\pi$
$458$	10.1536	−	6.52532i	0.474446	−	0.304908i
$459$	−1.28811	−	3.18408i	−0.0601240	−	0.148620i
$460$	−1.20514	+	4.64194i	−0.0561900	+	0.216432i
$461$		−	10.4166i		−	0.485148i	−0.970133	−	0.242574i	$-0.922008\pi$
$461$		−	10.4166i		−	0.485148i	0.970133	−	0.242574i	$-0.0779917\pi$
$462$	4.66108	−	12.8545i	0.216853	−	0.598044i
$463$	−0.558795	+	3.88651i	−0.0259694	+	0.180621i	−0.998678	−	0.0514106i	$-0.983628\pi$
$463$	−0.558795	+	3.88651i	−0.0259694	+	0.180621i	0.972708	+	0.232032i	$0.0745374\pi$
$464$	6.52326	+	2.97907i	0.302835	+	0.138300i
$465$	−5.80724	+	7.90720i	−0.269304	+	0.366688i
$466$	8.54256	+	18.7056i	0.395727	+	0.866520i
$467$	−15.7175	−	18.1389i	−0.727318	−	0.839369i	0.264849	−	0.964290i	$-0.414678\pi$
$467$	−15.7175	−	18.1389i	−0.727318	−	0.839369i	−0.992167	+	0.124920i	$0.960132\pi$
$468$	−3.11377	−	0.389738i	−0.143934	−	0.0180157i
$469$	6.92174	+	2.03241i	0.319616	+	0.0938478i
$470$	−1.73657	+	2.00411i	−0.0801020	+	0.0924426i
$471$	0.552488	+	6.84492i	0.0254573	+	0.315397i
$472$	−7.65503	−	4.91959i	−0.352351	−	0.226442i
$473$	18.1108	+	15.6931i	0.832734	+	0.721568i
$474$	−10.5864	+	4.05914i	−0.486251	+	0.186443i
$475$	−0.735580	+	0.105760i	−0.0337507	+	0.00485262i
$476$	1.04270	−	0.903504i	0.0477921	−	0.0414121i
$477$	−18.0968	+	2.94053i	−0.828595	+	0.134637i
$478$	6.50428	−	1.90983i	0.297499	−	0.0873535i
$479$	6.99214	−	15.3107i	0.319479	−	0.699562i	−0.679953	−	0.733256i	$-0.738000\pi$
$479$	6.99214	−	15.3107i	0.319479	−	0.699562i	0.999432	+	0.0336938i	$0.0107271\pi$
$480$	−1.51253	+	0.843944i	−0.0690374	+	0.0385206i
$481$	−2.08408	−	3.24289i	−0.0950258	−	0.147863i
$482$	30.2606			1.37833
$483$	15.5426	+	7.68259i	0.707213	+	0.349570i
$484$	−3.30546			−0.150248
$485$	−8.70523	−	13.5456i	−0.395284	−	0.615074i
$486$	15.5833	+	0.400528i	0.706873	+	0.0181683i
$487$	14.6989	−	32.1861i	0.666071	−	1.45849i	−0.210684	−	0.977554i	$-0.567569\pi$
$487$	14.6989	−	32.1861i	0.666071	−	1.45849i	0.876755	−	0.480937i	$-0.159703\pi$
$488$	−11.4630	+	3.36585i	−0.518908	+	0.152365i
$489$	3.51399	+	1.87729i	0.158908	+	0.0848942i
$490$	1.99786	−	1.73116i	0.0902543	−	0.0782058i
$491$	−30.2997	+	4.35643i	−1.36740	+	0.196603i	−0.786611	−	0.617448i	$-0.788166\pi$
$491$	−30.2997	+	4.35643i	−1.36740	+	0.196603i	−0.580793	+	0.814051i	$0.697257\pi$
$492$	−7.50490	−	19.5731i	−0.338347	−	0.882424i
$493$	−3.58255	−	3.10430i	−0.161350	−	0.139810i
$494$	−0.653945	−	0.420265i	−0.0294224	−	0.0189086i
$495$	8.43805	−	7.58607i	0.379262	−	0.340968i
$496$	−3.70923	+	4.28068i	−0.166549	+	0.192208i
$497$	−20.8776	−	6.13020i	−0.936486	−	0.274977i
$498$	1.82704	−	1.86075i	0.0818718	−	0.0833823i
$499$	1.66760	+	1.92452i	0.0746522	+	0.0861532i	0.791847	−	0.610720i	$-0.209120\pi$
$499$	1.66760	+	1.92452i	0.0746522	+	0.0861532i	−0.717195	+	0.696873i	$0.754574\pi$
$500$	−0.415415	−	0.909632i	−0.0185779	−	0.0406800i
$501$	−27.1591	−	19.9463i	−1.21338	−	0.891134i
$502$	−13.1251	−	5.99405i	−0.585804	−	0.267528i
$503$	4.12449	−	28.6864i	0.183902	−	1.27907i	−0.663526	−	0.748154i	$-0.730941\pi$
$503$	4.12449	−	28.6864i	0.183902	−	1.27907i	0.847427	−	0.530911i	$-0.178150\pi$
$504$	1.87364	+	5.97474i	0.0834585	+	0.266136i
$505$		−	2.93530i		−	0.130619i
$506$	2.01313	−	18.0270i	0.0894947	−	0.801398i
$507$	−16.3947	+	12.5084i	−0.728115	+	0.555517i
$508$	9.09044	−	5.84207i	0.403323	−	0.259200i
$509$	−11.2676	−	1.62003i	−0.499426	−	0.0718065i	−0.112001	−	0.993708i	$-0.535726\pi$
$509$	−11.2676	−	1.62003i	−0.499426	−	0.0718065i	−0.387424	+	0.921902i	$0.626635\pi$
$510$	1.11649	−	0.253586i	0.0494388	−	0.0112290i
$511$	6.81644	+	23.2147i	0.301542	+	1.02696i
$512$	−0.909632	+	0.415415i	−0.0402004	+	0.0183589i
$513$	3.43862	+	1.75700i	0.151819	+	0.0775732i
$514$	1.67722	+	11.6653i	0.0739788	+	0.514534i
$515$	−0.572424	+	1.94950i	−0.0252240	+	0.0859052i
$516$	−10.9528	−	0.682797i	−0.482171	−	0.0300585i
$517$	5.42254	−	8.43764i	0.238483	−	0.371087i
$518$	−4.15852	+	6.47079i	−0.182715	+	0.284310i
$519$	25.7491	+	1.60519i	1.13026	+	0.0704601i
$520$	0.294699	−	1.00365i	0.0129234	−	0.0440130i
$521$	5.88997	+	40.9657i	0.258044	+	1.79474i	0.546724	+	0.837313i	$0.315875\pi$
$521$	5.88997	+	40.9657i	0.258044	+	1.79474i	−0.288679	+	0.957426i	$0.593216\pi$
$522$	19.4031	−	9.29347i	0.849252	−	0.406764i
$523$	22.9961	−	10.5020i	1.00555	−	0.459219i	0.156582	−	0.987665i	$-0.449952\pi$
$523$	22.9961	−	10.5020i	1.00555	−	0.459219i	0.848967	+	0.528446i	$0.177225\pi$
$524$	2.86214	+	9.74754i	0.125033	+	0.425823i
$525$	−3.52537	+	0.800713i	−0.153860	+	0.0349460i
$526$	17.4658	+	2.51120i	0.761544	+	0.109493i
$527$	3.14976	−	2.02423i	0.137206	−	0.0881766i
$528$	5.20829	−	3.97368i	0.226662	−	0.172932i
$529$	22.4334	+	5.07370i	0.975365	+	0.220595i
$530$		−	6.11138i		−	0.265461i
$531$	−26.0479	+	8.16844i	−1.13038	+	0.354480i
$532$	−0.220744	+	1.53531i	−0.00957048	+	0.0665642i
$533$	11.5157	+	5.25906i	0.498801	+	0.227795i
$534$	−11.3120	−	8.30778i	−0.489516	−	0.359513i
$535$	2.96180	+	6.48545i	0.128050	+	0.280390i
$536$	2.26337	+	2.61207i	0.0977628	+	0.112824i
$537$	24.9029	−	25.3623i	1.07464	−	1.09447i
$538$	15.8052	+	4.64083i	0.681411	+	0.200080i
$539$	−6.54769	+	7.55643i	−0.282029	+	0.325479i
$540$	−0.964892	+	5.10578i	−0.0415223	+	0.219718i
$541$	30.6413	+	19.6920i	1.31737	+	0.846624i	0.994989	−	0.0999857i	$-0.0318797\pi$
$541$	30.6413	+	19.6920i	1.31737	+	0.846624i	0.322383	+	0.946609i	$0.395516\pi$
$542$	−6.00168	−	5.20049i	−0.257794	−	0.223380i
$543$	14.9944	+	39.1060i	0.643470	+	1.67820i
$544$	0.654293	−	0.0940731i	0.0280526	−	0.00403335i
$545$	2.67267	−	2.31588i	0.114485	−	0.0992016i
$546$	−3.33540	−	1.78188i	−0.142742	−	0.0762576i
$547$	4.65073	−	1.36558i	0.198851	−	0.0583878i	−0.180791	−	0.983522i	$-0.557866\pi$
$547$	4.65073	−	1.36558i	0.198851	−	0.0583878i	0.379641	+	0.925134i	$0.376047\pi$
$548$	−1.67187	+	3.66088i	−0.0714187	+	0.156385i
$549$	−14.2904	+	32.8688i	−0.609900	+	1.40281i
$550$	2.04484	+	3.18184i	0.0871923	+	0.135674i
$551$	5.32933			0.227037
$552$	4.27449	+	7.12241i	0.181934	+	0.303150i
$553$	−13.6628			−0.581002
$554$	−14.9083	−	23.1977i	−0.633392	−	0.985577i
$555$	−5.57403	+	3.11013i	−0.236604	+	0.132017i
$556$	4.26586	−	9.34093i	0.180913	−	0.396144i
$557$	33.1365	−	9.72976i	1.40404	−	0.412263i	0.509970	−	0.860192i	$-0.329657\pi$
$557$	33.1365	−	9.72976i	1.40404	−	0.412263i	0.894069	+	0.447929i	$0.147838\pi$
$558$	2.72534	+	16.7725i	0.115373	+	0.710036i
$559$	5.00872	−	4.34008i	0.211846	−	0.183566i
$560$	−2.06597	+	0.297041i	−0.0873030	+	0.0125523i
$561$	−4.04335	+	1.55034i	−0.170710	+	0.0654553i
$562$	0.306961	+	0.265983i	0.0129484	+	0.0112198i
$563$	14.4681	+	9.29809i	0.609758	+	0.391868i	0.808766	−	0.588130i	$-0.200136\pi$
$563$	14.4681	+	9.29809i	0.609758	+	0.391868i	−0.199008	+	0.979998i	$0.563772\pi$
$564$	0.369529	+	4.57819i	0.0155600	+	0.192776i
$565$	−5.94818	+	6.86457i	−0.250242	+	0.288794i
$566$	−19.8756	−	5.83599i	−0.835432	−	0.245305i
$567$	17.3612	+	7.17369i	0.729101	+	0.301267i
$568$	−6.82685	−	7.87861i	−0.286448	−	0.330579i
$569$	−5.51954	−	12.0861i	−0.231391	−	0.506676i	0.757946	−	0.652317i	$-0.226203\pi$
$569$	−5.51954	−	12.0861i	−0.231391	−	0.506676i	−0.989338	+	0.145641i	$0.953476\pi$
$570$	−0.761918	+	1.03744i	−0.0319132	+	0.0434534i
$571$	34.6334	+	15.8166i	1.44936	+	0.661902i	0.975761	−	0.218837i	$-0.0702262\pi$
$571$	34.6334	+	15.8166i	1.44936	+	0.661902i	0.473602	+	0.880739i	$0.342954\pi$
$572$	−0.563044	+	3.91606i	−0.0235420	+	0.163739i
$573$	−4.26842	+	11.7716i	−0.178316	+	0.491765i
$574$		−	25.2610i		−	1.05437i
$575$	−4.29735	+	2.12904i	−0.179212	+	0.0887871i
$576$	−0.792437	+	2.89345i	−0.0330182	+	0.120560i
$577$	11.2840	−	7.25179i	0.469759	−	0.301896i	−0.284261	−	0.958747i	$-0.591748\pi$
$577$	11.2840	−	7.25179i	0.469759	−	0.301896i	0.754020	+	0.656851i	$0.228112\pi$
$578$	16.3945	+	2.35717i	0.681920	+	0.0980453i
$579$	−9.23901	−	40.6773i	−0.383960	−	1.69049i
$580$	2.02039	+	6.88083i	0.0838923	+	0.285711i
$581$	2.85852	−	1.30544i	0.118591	−	0.0541589i
$582$	−27.3047	−	5.67888i	−1.13181	−	0.235397i
$583$	3.28958	+	22.8795i	0.136240	+	0.947573i
$584$	−3.26581	+	11.1223i	−0.135140	+	0.460246i
$585$	−1.74454	−	2.60846i	−0.0721280	−	0.107846i
$586$	−12.0203	+	18.7039i	−0.496554	+	0.772653i
$587$	−6.38911	+	9.94166i	−0.263707	+	0.410336i	−0.947705	−	0.319148i	$-0.896603\pi$
$587$	−6.38911	+	9.94166i	−0.263707	+	0.410336i	0.683998	+	0.729484i	$0.260240\pi$
$588$	0.284886	−	4.56990i	0.0117485	−	0.188459i
$589$	−1.18589	+	4.03878i	−0.0488638	+	0.166415i
$590$	−1.29500	−	9.00693i	−0.0533143	−	0.370809i
$591$	3.96787	−	19.0780i	0.163217	−	0.784762i
$592$	−3.35220	+	1.53090i	−0.137775	+	0.0629195i
$593$	0.241084	+	0.821056i	0.00990012	+	0.0337167i	0.964295	−	0.264831i	$-0.0853161\pi$
$593$	0.241084	+	0.821056i	0.00990012	+	0.0337167i	−0.954395	+	0.298547i	$0.903498\pi$
$594$	0.864028	−	19.6342i	0.0354515	−	0.805600i
$595$	1.36565	+	0.196350i	0.0559860	+	0.00804958i
$596$	−3.89009	+	2.50001i	−0.159344	+	0.102404i
$597$	−2.03941	−	2.67305i	−0.0834673	−	0.109400i
$598$	−4.85558	−	1.26061i	−0.198559	−	0.0515500i
$599$			21.1464i			0.864018i	0.901869	+	0.432009i	$0.142195\pi$
$599$			21.1464i			0.864018i	−0.901869	+	0.432009i	$0.857805\pi$
$600$	−1.62831	−	0.590431i	−0.0664755	−	0.0241042i
$601$	−5.03858	+	35.0441i	−0.205528	+	1.42948i	0.581994	+	0.813193i	$0.302273\pi$
$601$	−5.03858	+	35.0441i	−0.205528	+	1.42948i	−0.787522	+	0.616286i	$0.788636\pi$
$602$	−12.0293	−	5.49359i	−0.490277	−	0.223902i
$603$	10.3671	−	0.189544i	0.422180	−	0.00771883i
$604$	1.14338	+	2.50364i	0.0465233	+	0.101872i
$605$	−2.16461	−	2.49810i	−0.0880041	−	0.101562i
$606$	−3.62771	−	3.56199i	−0.147366	−	0.144696i
$607$	3.12684	+	0.918124i	0.126915	+	0.0372655i	0.344573	−	0.938760i	$-0.388024\pi$
$607$	3.12684	+	0.918124i	0.126915	+	0.0372655i	−0.217658	+	0.976025i	$0.569842\pi$
$608$	−0.486656	+	0.561631i	−0.0197365	+	0.0227771i
$609$	25.8414	−	2.08579i	1.04715	−	0.0845204i
$610$	−10.0504	−	6.45903i	−0.406931	−	0.261518i
$611$	−2.09634	−	1.81649i	−0.0848089	−	0.0734874i
$612$	1.04145	−	1.68758i	0.0420981	−	0.0682163i
$613$	0.946960	−	0.136152i	0.0382474	−	0.00549914i	−0.123165	−	0.992386i	$-0.539304\pi$
$613$	0.946960	−	0.136152i	0.0382474	−	0.00549914i	0.161412	+	0.986887i	$0.448395\pi$
$614$	−4.61422	+	3.99824i	−0.186215	+	0.161356i
$615$	9.87771	−	18.4895i	0.398308	−	0.745568i
$616$	7.57459	−	2.22410i	0.305189	−	0.0896115i
$617$	12.6138	−	27.6204i	0.507813	−	1.11196i	−0.466037	−	0.884765i	$-0.654319\pi$
$617$	12.6138	−	27.6204i	0.507813	−	1.11196i	0.973850	−	0.227190i	$-0.0729539\pi$
$618$	1.71473	+	3.07317i	0.0689764	+	0.123621i
$619$	19.3858	+	30.1650i	0.779183	+	1.21243i	0.972866	+	0.231368i	$0.0743202\pi$
$619$	19.3858	+	30.1650i	0.779183	+	1.21243i	−0.193683	+	0.981064i	$0.562043\pi$
$620$	−5.66415			−0.227478
$621$	24.6204	+	3.85182i	0.987982	+	0.154568i
$622$	−13.1290			−0.526424
$623$	−9.14376	−	14.2280i	−0.366337	−	0.570032i
$624$	−0.882785	−	1.58214i	−0.0353397	−	0.0633365i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	−8.32229	+	2.44364i	−0.332626	+	0.0976677i
$627$	2.29401	−	4.29403i	0.0916141	−	0.171487i
$628$	−2.99637	+	2.59637i	−0.119568	+	0.103607i
$629$	2.41122	−	0.346681i	0.0961415	−	0.0138231i
$630$	−3.28843	+	5.32862i	−0.131014	+	0.212297i
$631$	−22.0520	−	19.1082i	−0.877878	−	0.760686i	0.0941481	−	0.995558i	$-0.469987\pi$
$631$	−22.0520	−	19.1082i	−0.877878	−	0.760686i	−0.972026	+	0.234872i	$0.924533\pi$
$632$	−5.50682	−	3.53902i	−0.219049	−	0.140775i
$633$	3.58255	−	0.289166i	0.142393	−	0.0114933i
$634$	19.8888	−	22.9528i	0.789883	−	0.911574i
$635$	10.3681	+	3.04435i	0.411446	+	0.120812i
$636$	−7.55299	−	7.41615i	−0.299495	−	0.294070i
$637$	1.81083	+	2.08981i	0.0717478	+	0.0828013i
$638$	−11.2676	−	24.6726i	−0.446089	−	0.976799i
$639$	−31.2695	+	0.571709i	−1.23700	+	0.0226164i
$640$	−0.909632	−	0.415415i	−0.0359564	−	0.0164207i
$641$	1.28966	−	8.96978i	0.0509385	−	0.354285i	−0.948372	−	0.317160i	$-0.897271\pi$
$641$	1.28966	−	8.96978i	0.0509385	−	0.354285i	0.999311	−	0.0371252i	$-0.0118200\pi$
$642$	11.6094	+	4.20962i	0.458188	+	0.166141i
$643$		−	38.2327i		−	1.50775i	−0.657018	−	0.753875i	$-0.728182\pi$
$643$		−	38.2327i		−	1.50775i	0.657018	−	0.753875i	$-0.271818\pi$
$644$	1.73676	+	9.85809i	0.0684380	+	0.388463i
$645$	−6.65655	−	8.72473i	−0.262102	−	0.343536i
$646$	0.413252	−	0.265581i	0.0162592	−	0.0104491i
$647$	15.7571	+	2.26553i	0.619477	+	0.0890673i	0.444906	−	0.895577i	$-0.353237\pi$
$647$	15.7571	+	2.26553i	0.619477	+	0.0890673i	0.174571	+	0.984645i	$0.444146\pi$
$648$	5.13928	+	7.38836i	0.201890	+	0.290242i
$649$	9.69634	+	33.0227i	0.380614	+	1.29625i
$650$	0.951496	−	0.434534i	0.0373207	−	0.0170438i
$651$	−4.16958	+	20.0478i	−0.163419	+	0.785734i
$652$	0.327349	+	2.27676i	0.0128200	+	0.0891648i
$653$	−6.58852	+	22.4384i	−0.257829	+	0.878084i	0.724238	+	0.689550i	$0.242192\pi$
$653$	−6.58852	+	22.4384i	−0.257829	+	0.878084i	−0.982067	+	0.188534i	$0.939626\pi$
$654$	0.381111	−	6.11345i	0.0149026	−	0.239055i
$655$	−5.49240	+	8.54634i	−0.214606	+	0.333933i
$656$	6.54325	−	10.1815i	0.255471	−	0.397520i
$657$	19.3328	+	28.9066i	0.754245	+	1.12775i
$658$	−1.55936	+	5.31069i	−0.0607902	+	0.207032i
$659$	−0.220335	−	1.53247i	−0.00858304	−	0.0596964i	0.985080	−	0.172098i	$-0.0550547\pi$
$659$	−0.220335	−	1.53247i	−0.00858304	−	0.0596964i	−0.993663	+	0.112402i	$0.964146\pi$
$660$	6.41381	+	1.33396i	0.249657	+	0.0519242i
$661$	−13.4064	+	6.12248i	−0.521447	+	0.238137i	−0.658709	−	0.752398i	$-0.728897\pi$
$661$	−13.4064	+	6.12248i	−0.521447	+	0.238137i	0.137262	+	0.990535i	$0.456170\pi$
$662$	−0.254911	−	0.868148i	−0.00990741	−	0.0337415i
$663$	0.265257	+	1.16787i	0.0103017	+	0.0453563i
$664$	1.49027	+	0.214269i	0.0578339	+	0.00831525i
$665$	−1.30487	+	0.838587i	−0.0506006	+	0.0325190i
$666$	−2.92031	+	10.6630i	−0.113160	+	0.413183i
$667$	32.6768	−	10.7268i	1.26525	−	0.415344i
$668$		−	19.4548i		−	0.752730i
$669$	5.31744	−	14.6646i	0.205584	−	0.566966i
$670$	−0.491878	+	3.42109i	−0.0190029	+	0.132168i
$671$	41.1031	+	18.7712i	1.58677	+	0.724653i
$672$	−2.13994	+	2.91376i	−0.0825499	+	0.112401i
$673$	−2.36834	−	5.18594i	−0.0912928	−	0.199903i	0.858477	−	0.512851i	$-0.171411\pi$
$673$	−2.36834	−	5.18594i	−0.0912928	−	0.199903i	−0.949770	+	0.312948i	$0.898683\pi$
$674$	17.5818	+	20.2905i	0.677228	+	0.781562i
$675$	−4.49056	+	2.61436i	−0.172842	+	0.100627i
$676$	−11.4236	−	3.35426i	−0.439368	−	0.129010i
$677$	8.01771	−	9.25293i	0.308146	−	0.355619i	−0.580462	−	0.814287i	$-0.697128\pi$
$677$	8.01771	−	9.25293i	0.308146	−	0.355619i	0.888608	+	0.458668i	$0.151673\pi$
$678$	1.26573	+	15.6814i	0.0486100	+	0.602242i
$679$	−28.2725	−	18.1697i	−1.08500	−	0.697287i
$680$	0.499566	+	0.432877i	0.0191575	+	0.0166001i
$681$	−27.6487	+	10.6013i	−1.05950	+	0.406244i
$682$	21.2052	−	3.04885i	0.811989	−	0.116746i
$683$	25.5249	−	22.1175i	0.976685	−	0.846302i	−0.0114433	−	0.999935i	$-0.503643\pi$
$683$	25.5249	−	22.1175i	0.976685	−	0.846302i	0.988128	+	0.153632i	$0.0490972\pi$
$684$	0.357568	+	2.20057i	0.0136720	+	0.0841410i
$685$	−3.86155	+	1.13385i	−0.147542	+	0.0433223i
$686$	8.36152	−	18.3092i	0.319244	−	0.699048i
$687$	18.2557	−	10.1861i	0.696498	−	0.388623i
$688$	−3.42544	−	5.33009i	−0.130594	−	0.203208i
$689$	6.39264			0.243540
$690$	−2.58357	+	7.89463i	−0.0983547	+	0.300543i
$691$	−24.1473			−0.918608			−0.459304	−	0.888279i	$-0.651901\pi$
$691$	−24.1473			−0.918608			−0.459304	+	0.888279i	$0.651901\pi$
$692$	8.05290	+	12.5305i	0.306125	+	0.476340i
$693$	9.44286	−	21.7191i	0.358704	−	0.825042i
$694$	−2.00953	+	4.40025i	−0.0762806	+	0.167031i
$695$	9.85294	−	2.89309i	0.373743	−	0.109741i
$696$	10.9557	+	5.85290i	0.415274	+	0.221854i
$697$	−6.04613	+	5.23900i	−0.229013	+	0.198441i
$698$	−19.5318	+	2.80825i	−0.739289	+	0.106294i
$699$	12.7516	+	33.2569i	0.482312	+	1.25789i
$700$	−1.57741	−	1.36683i	−0.0596204	−	0.0516614i
$701$	−27.6474	−	17.7679i	−1.04423	−	0.671086i	−0.0982003	−	0.995167i	$-0.531309\pi$
$701$	−27.6474	−	17.7679i	−1.04423	−	0.671086i	−0.946029	+	0.324081i	$0.894945\pi$
$702$	−5.34076	−	1.00930i	−0.201574	−	0.0380935i
$703$	−1.79344	+	2.06974i	−0.0676408	+	0.0780616i
$704$	3.62905	+	1.06558i	0.136775	+	0.0401607i
$705$	−3.21797	+	3.27735i	−0.121196	+	0.123432i
$706$	−20.9205	−	24.1436i	−0.787355	−	0.908656i
$707$	−2.54508	−	5.57295i	−0.0957176	−	0.209592i
$708$	−12.7030	−	9.32942i	−0.477409	−	0.350621i
$709$	16.1299	+	7.36626i	0.605770	+	0.276646i	0.694594	−	0.719401i	$-0.255584\pi$
$709$	16.1299	+	7.36626i	0.605770	+	0.276646i	−0.0888247	+	0.996047i	$0.528311\pi$
$710$	1.48362	−	10.3188i	0.0556792	−	0.387257i
$711$	−18.7381	+	5.87616i	−0.702735	+	0.220373i
$712$		−	8.10308i		−	0.303676i
$713$	0.857902	+	27.1508i	0.0321287	+	1.01680i
$714$	1.89988	−	1.44952i	0.0711011	−	0.0542468i
$715$	−3.32827	+	2.13895i	−0.124470	+	0.0799922i
$716$	20.3127	+	2.92052i	0.759120	+	0.109145i
$717$	11.4497	−	2.60057i	0.427598	−	0.0971200i
$718$	0.896172	+	3.05208i	0.0334448	+	0.113903i
$719$	39.9894	−	18.2626i	1.49135	−	0.681079i	0.507764	−	0.861496i	$-0.330472\pi$
$719$	39.9894	−	18.2626i	1.49135	−	0.681079i	0.983590	+	0.180417i	$0.0577448\pi$
$720$	−2.70566	+	1.29592i	−0.100834	+	0.0482961i
$721$	0.603528	+	4.19763i	0.0224766	+	0.156328i
$722$	5.19733	−	17.7005i	0.193425	−	0.658743i
$723$	52.3113	+	3.26108i	1.94548	+	0.121281i
$724$	−13.0730	+	20.3421i	−0.485856	+	0.756007i
$725$	−3.87711	+	6.03290i	−0.143992	+	0.224056i
$726$	−5.71413	−	0.356217i	−0.212071	−	0.0132205i
$727$	7.58333	−	25.8265i	0.281250	−	0.957851i	−0.690794	−	0.723052i	$-0.742739\pi$
$727$	7.58333	−	25.8265i	0.281250	−	0.957851i	0.972044	−	0.234799i	$-0.0754431\pi$
$728$	−0.310712	−	2.16105i	−0.0115157	−	0.0800937i
$729$	26.8956	+	2.37175i	0.996134	+	0.0878425i
$730$	−10.5444	+	4.81545i	−0.390264	+	0.178228i
$731$	1.17994	+	4.01851i	0.0436417	+	0.148630i
$732$	−20.1788	+	4.58320i	−0.745831	+	0.169400i
$733$	−12.2134	−	1.75602i	−0.451111	−	0.0648600i	−0.0869850	−	0.996210i	$-0.527723\pi$
$733$	−12.2134	−	1.75602i	−0.451111	−	0.0648600i	−0.364126	+	0.931350i	$0.618632\pi$
$734$	25.1189	−	16.1429i	0.927156	−	0.595847i
$735$	3.64026	−	2.77734i	0.134273	−	0.102444i
$736$	−1.85349	+	4.42319i	−0.0683206	+	0.163041i
$737$		−	13.0725i		−	0.481531i
$738$	−10.8644	−	34.6447i	−0.399922	−	1.27529i
$739$	1.88621	−	13.1189i	0.0693855	−	0.482587i	−0.925268	−	0.379315i	$-0.876160\pi$
$739$	1.88621	−	13.1189i	0.0693855	−	0.482587i	0.994653	−	0.103272i	$-0.0329312\pi$
$740$	−3.35220	−	1.53090i	−0.123229	−	0.0562769i
$741$	−1.08518	−	0.796983i	−0.0398651	−	0.0292779i
$742$	−5.29892	−	11.6030i	−0.194530	−	0.425960i
$743$	−14.5944	−	16.8428i	−0.535416	−	0.617903i	0.422007	−	0.906593i	$-0.361326\pi$
$743$	−14.5944	−	16.8428i	−0.535416	−	0.617903i	−0.957423	+	0.288690i	$0.906780\pi$
$744$	−6.87344	+	7.00026i	−0.251993	+	0.256642i
$745$	−4.43685	−	1.30278i	−0.162554	−	0.0477300i
$746$	−24.0641	+	27.7714i	−0.881049	+	1.01678i
$747$	3.35893	−	3.01978i	0.122897	−	0.110488i
$748$	−2.10326	−	1.35168i	−0.0769028	−	0.0494224i
$749$	11.2465	+	9.74517i	0.410939	+	0.356081i
$750$	−0.620098	−	1.61724i	−0.0226428	−	0.0590534i
$751$	3.38314	−	0.486422i	0.123452	−	0.0177498i	−0.0803117	−	0.996770i	$-0.525592\pi$
$751$	3.38314	−	0.486422i	0.123452	−	0.0177498i	0.203764	+	0.979020i	$0.434682\pi$
$752$	−2.00411	+	1.73657i	−0.0730823	+	0.0633262i
$753$	−22.0434	−	11.7763i	−0.803306	−	0.429154i
$754$	−7.19750	+	2.11338i	−0.262118	+	0.0769647i
$755$	−1.14338	+	2.50364i	−0.0416117	+	0.0911169i
$756$	2.59507	+	10.5304i	0.0943819	+	0.382988i
$757$	−3.87928	−	6.03627i	−0.140995	−	0.219392i	0.763574	−	0.645721i	$-0.223443\pi$
$757$	−3.87928	−	6.03627i	−0.140995	−	0.219392i	−0.904568	+	0.426329i	$0.859807\pi$
$758$	6.32764			0.229830
$759$	5.42280	−	30.9462i	0.196835	−	1.12328i
$760$	−0.743144			−0.0269567
$761$	18.9528	+	29.4911i	0.687037	+	1.06905i	0.993126	+	0.117048i	$0.0373431\pi$
$761$	18.9528	+	29.4911i	0.687037	+	1.06905i	−0.306089	+	0.952003i	$0.599020\pi$
$762$	16.3442	−	9.11952i	0.592087	−	0.330365i
$763$	3.06631	−	6.71429i	0.111008	−	0.243074i
$764$	−6.93649	+	2.03674i	−0.250954	+	0.0736866i
$765$	1.95739	−	0.318054i	0.0707696	−	0.0114993i
$766$	−5.57971	+	4.83485i	−0.201603	+	0.174690i
$767$	9.42145	−	1.35460i	0.340189	−	0.0489118i
$768$	−1.61724	+	0.620098i	−0.0583573	+	0.0223759i
$769$	23.4998	+	20.3627i	0.847424	+	0.734297i	0.965971	−	0.258651i	$-0.0832780\pi$
$769$	23.4998	+	20.3627i	0.847424	+	0.734297i	−0.118546	+	0.992949i	$0.537823\pi$
$770$	6.64116	+	4.26801i	0.239331	+	0.153809i
$771$	1.64227	+	20.3465i	0.0591448	+	0.732761i
$772$	15.7712	−	18.2009i	0.567616	−	0.655064i
$773$	−48.8089	−	14.3316i	−1.75553	−	0.515471i	−0.763987	−	0.645231i	$-0.776761\pi$
$773$	−48.8089	−	14.3316i	−1.75553	−	0.515471i	−0.991545	+	0.129760i	$0.958579\pi$
$774$	−18.8605	−	2.36070i	−0.677927	−	0.0848534i
$775$	−3.70923	−	4.28068i	−0.133239	−	0.153767i
$776$	−6.68889	−	14.6466i	−0.240117	−	0.525783i
$777$	−7.88615	+	10.7379i	−0.282914	+	0.385219i
$778$	−13.9201	−	6.35712i	−0.499062	−	0.227914i
$779$	1.27999	−	8.90255i	0.0458605	−	0.318967i
$780$	0.617604	−	1.70325i	0.0221138	−	0.0609861i
$781$			39.4296i			1.41090i
$782$	1.99930	−	2.46020i	0.0714949	−	0.0879767i
$783$	34.5436	−	13.9746i	1.23449	−	0.499410i
$784$	2.22390	−	1.42921i	0.0794249	−	0.0510433i
$785$	−3.92441	−	0.564246i	−0.140068	−	0.0201388i
$786$	3.89730	+	17.1590i	0.139012	+	0.612040i
$787$	2.34075	+	7.97186i	0.0834387	+	0.284166i	0.990634	−	0.136543i	$-0.0435993\pi$
$787$	2.34075	+	7.97186i	0.0834387	+	0.284166i	−0.907195	+	0.420710i	$0.861781\pi$
$788$	10.2337	−	4.67357i	0.364560	−	0.166489i
$789$	29.9224	+	6.22332i	1.06526	+	0.221556i
$790$	−0.931588	−	6.47934i	−0.0331444	−	0.230525i
$791$	−5.34120	+	18.1904i	−0.189911	+	0.646778i
$792$	9.43177	−	6.30799i	0.335143	−	0.224145i
$793$	6.75629	−	10.5130i	0.239923	−	0.373327i
$794$	0.753961	−	1.17319i	0.0267571	−	0.0416348i
$795$	0.658602	−	10.5647i	0.0233582	−	0.374692i
$796$	0.546889	−	1.86253i	0.0193840	−	0.0660157i
$797$	2.83260	+	19.7012i	0.100336	+	0.697851i	0.976449	+	0.215746i	$0.0692185\pi$
$797$	2.83260	+	19.7012i	0.100336	+	0.697851i	−0.876114	+	0.482105i	$0.839872\pi$
$798$	−0.547055	+	2.63030i	−0.0193655	+	0.0931114i
$799$	1.59450	−	0.728183i	0.0564093	−	0.0257613i
$800$	−0.281733	−	0.959493i	−0.00996075	−	0.0339232i
$801$	−18.6596	−	15.5807i	−0.659305	−	0.550516i
$802$	11.6045	+	1.66847i	0.409768	+	0.0589158i
$803$	36.8835	−	23.7036i	1.30159	−	0.836482i
$804$	3.63119	+	4.75939i	0.128062	+	0.167851i
$805$	−6.31291	+	7.76823i	−0.222501	+	0.273794i
$806$		−	5.92483i		−	0.208693i
$807$	26.8222	+	9.72584i	0.944188	+	0.342366i
$808$	0.417737	−	2.90543i	0.0146959	−	0.102213i
$809$	3.92490	+	1.79244i	0.137992	+	0.0630188i	0.483214	−	0.875502i	$-0.339469\pi$
$809$	3.92490	+	1.79244i	0.137992	+	0.0630188i	−0.345222	+	0.938521i	$0.612196\pi$
$810$	−2.21824	+	8.72235i	−0.0779409	+	0.306472i
$811$	17.4883	+	38.2941i	0.614098	+	1.34469i	0.919736	+	0.392538i	$0.128403\pi$
$811$	17.4883	+	38.2941i	0.614098	+	1.34469i	−0.305638	+	0.952148i	$0.598870\pi$
$812$	9.80199	+	11.3121i	0.343982	+	0.396977i
$813$	−9.81464	−	9.63684i	−0.344214	−	0.337979i
$814$	13.3739	+	3.92692i	0.468754	+	0.137638i
$815$	−1.50629	+	1.73835i	−0.0527631	+	0.0608919i
$816$	1.14121	−	0.0921128i	0.0399503	−	0.00322459i
$817$	−3.96103	−	2.54560i	−0.138579	−	0.0890593i
$818$	24.2788	+	21.0377i	0.848887	+	0.735564i
$819$	−5.57386	−	3.43978i	−0.194766	−	0.120196i
$820$	11.9796	−	1.72240i	0.418345	−	0.0601489i
$821$	−7.08830	+	6.14205i	−0.247383	+	0.214359i	−0.769722	−	0.638379i	$-0.779605\pi$
$821$	−7.08830	+	6.14205i	−0.247383	+	0.214359i	0.522339	+	0.852738i	$0.325060\pi$
$822$	−3.28467	+	6.14838i	−0.114566	+	0.214449i
$823$	−34.6336	+	10.1693i	−1.20725	+	0.354481i	−0.822621	−	0.568590i	$-0.807489\pi$
$823$	−34.6336	+	10.1693i	−1.20725	+	0.354481i	−0.384630	+	0.923071i	$0.625671\pi$
$824$	−0.844041	+	1.84819i	−0.0294035	+	0.0643848i
$825$	3.19201	+	5.72079i	0.111132	+	0.199172i
$826$	−10.2682	−	15.9776i	−0.357277	−	0.555933i
$827$	−12.7463			−0.443233			−0.221617	−	0.975134i	$-0.571133\pi$
$827$	−12.7463			−0.443233			−0.221617	+	0.975134i	$0.571133\pi$
$828$	6.62173	+	12.7731i	0.230121	+	0.443897i
$829$	−35.3008			−1.22605			−0.613024	−	0.790064i	$-0.710047\pi$
$829$	−35.3008			−1.22605			−0.613024	+	0.790064i	$0.710047\pi$
$830$	0.813988	+	1.26659i	0.0282539	+	0.0439640i
$831$	−23.2719	−	41.7084i	−0.807294	−	1.44685i
$832$	0.434534	−	0.951496i	0.0150647	−	0.0329872i
$833$	−1.67666	+	0.492312i	−0.0580928	+	0.0170576i
$834$	8.38101	−	15.6879i	0.290211	−	0.543227i
$835$	14.7030	−	12.7402i	0.508817	−	0.440893i
$836$	2.78215	−	0.400013i	0.0962228	−	0.0138347i
$837$	2.90377	+	29.2882i	0.100369	+	1.01235i
$838$	−16.5776	−	14.3645i	−0.572663	−	0.496215i
$839$	30.0405	+	19.3059i	1.03711	+	0.666513i	0.944272	−	0.329168i	$-0.106768\pi$
$839$	30.0405	+	19.3059i	1.03711	+	0.666513i	0.0928432	+	0.995681i	$0.470404\pi$
$840$	−3.60344	+	0.290852i	−0.124330	+	0.0100353i
$841$	14.6871	−	16.9498i	0.506451	−	0.584476i
$842$	18.7184	+	5.49623i	0.645080	+	0.189413i
$843$	0.501978	+	0.492884i	0.0172890	+	0.0169758i
$844$	1.35891	+	1.56826i	0.0467756	+	0.0539819i
$845$	−4.94586	−	10.8299i	−0.170143	−	0.372561i
$846$	0.145427	+	7.95411i	0.00499990	+	0.273468i
$847$	−6.27572	−	2.86602i	−0.215636	−	0.0984778i
$848$	0.869740	−	6.04918i	0.0298670	−	0.207730i
$849$	−33.7299	−	12.2306i	−1.15761	−	0.419752i
$850$			0.661021i			0.0226728i
$851$	−6.83054	+	16.3004i	−0.234148	+	0.558772i
$852$	−10.9525	−	14.3554i	−0.375226	−	0.491809i
$853$	5.80394	−	3.72997i	0.198723	−	0.127712i	−0.437495	−	0.899221i	$-0.644134\pi$
$853$	5.80394	−	3.72997i	0.198723	−	0.127712i	0.636218	+	0.771509i	$0.280498\pi$
$854$	−24.6821	−	3.54874i	−0.844603	−	0.121436i
$855$	−1.42892	+	1.71130i	−0.0488682	+	0.0585252i
$856$	2.00868	+	6.84094i	0.0686553	+	0.233819i
$857$	−3.77765	+	1.72519i	−0.129042	+	0.0589315i	−0.478890	−	0.877875i	$-0.658961\pi$
$857$	−3.77765	+	1.72519i	−0.129042	+	0.0589315i	0.349848	+	0.936807i	$0.386233\pi$
$858$	−1.39535	+	6.70899i	−0.0476365	+	0.229041i
$859$	−1.26342	−	8.78727i	−0.0431073	−	0.299818i	−0.999957	−	0.00923573i	$-0.997060\pi$
$859$	−1.26342	−	8.78727i	−0.0431073	−	0.299818i	0.956850	−	0.290582i	$-0.0938490\pi$
$860$	1.78503	−	6.07925i	0.0608689	−	0.207301i
$861$	2.72229	−	43.6686i	0.0927754	−	1.48822i
$862$	8.99403	−	13.9950i	0.306338	−	0.476671i
$863$	−3.97796	+	6.18983i	−0.135411	+	0.210704i	−0.902336	−	0.431032i	$-0.858149\pi$
$863$	−3.97796	+	6.18983i	−0.135411	+	0.210704i	0.766925	+	0.641737i	$0.221786\pi$
$864$	−1.68170	+	4.91649i	−0.0572126	+	0.167262i
$865$	−4.19643	+	14.2917i	−0.142683	+	0.485934i
$866$	−4.05287	−	28.1884i	−0.137722	−	0.957880i
$867$	28.0870	+	5.84160i	0.953885	+	0.198391i
$868$	−10.7539	+	4.91115i	−0.365012	+	0.166695i
$869$	6.97528	+	23.7556i	0.236620	+	0.805854i
$870$	2.75112	+	12.1126i	0.0932718	+	0.410655i
$871$	−3.57854	−	0.514516i	−0.121254	−	0.0174337i
$872$	2.97505	−	1.91195i	0.100748	−	0.0647468i
$873$	−46.5894	−	12.7596i	−1.57681	−	0.431846i
$874$	0.112558	+	3.56222i	0.00380733	+	0.120494i
$875$		−	2.08721i		−	0.0705606i
$876$	−6.84421	+	18.8752i	−0.231245	+	0.637734i
$877$	−4.49648	+	31.2737i	−0.151835	+	1.05604i	0.761305	+	0.648393i	$0.224559\pi$
$877$	−4.49648	+	31.2737i	−0.151835	+	1.05604i	−0.913141	+	0.407644i	$0.866350\pi$
$878$	−2.98757	−	1.36438i	−0.100826	−	0.0460455i
$879$	−22.7951	+	31.0380i	−0.768859	+	1.04689i
$880$	1.57121	+	3.44046i	0.0529653	+	0.115978i
$881$	−32.7643	−	37.8120i	−1.10386	−	1.27392i	−0.958672	−	0.284514i	$-0.908168\pi$
$881$	−32.7643	−	37.8120i	−1.10386	−	1.27392i	−0.145185	−	0.989404i	$-0.546378\pi$
$882$	0.984963	−	7.86926i	0.0331654	−	0.264972i
$883$	11.0904	+	3.25642i	0.373220	+	0.109587i	0.462963	−	0.886378i	$-0.346786\pi$
$883$	11.0904	+	3.25642i	0.373220	+	0.109587i	−0.0897428	+	0.995965i	$0.528605\pi$
$884$	−0.452799	+	0.522558i	−0.0152293	+	0.0175755i
$885$	−1.26802	−	15.7098i	−0.0426239	−	0.528079i
$886$	−31.5654	−	20.2858i	−1.06046	−	0.681516i
$887$	35.1807	+	30.4842i	1.18125	+	1.02356i	0.999189	+	0.0402737i	$0.0128230\pi$
$887$	35.1807	+	30.4842i	1.18125	+	1.02356i	0.182063	+	0.983287i	$0.441722\pi$
$888$	−5.95991	+	2.28520i	−0.200002	+	0.0766864i
$889$	22.3245	−	3.20978i	0.748739	−	0.107652i
$890$	6.12390	−	5.30639i	0.205273	−	0.177870i
$891$	3.60955	−	33.8484i	0.120924	−	1.13396i
$892$	8.64122	−	2.53729i	0.289330	−	0.0849548i
$893$	−0.818650	+	1.79259i	−0.0273951	+	0.0599869i
$894$	−6.99420	+	3.90253i	−0.233921	+	0.130520i
$895$	11.0948	+	17.2638i	0.370858	+	0.577066i
$896$	−2.08721			−0.0697288
$897$	−8.25796	−	2.70247i	−0.275725	−	0.0902329i
$898$	28.8025			0.961153
$899$	21.9605	+	34.1712i	0.732424	+	1.13967i
$900$	−2.75122	−	1.19615i	−0.0917074	−	0.0398717i
$901$	−1.67817	+	3.67469i	−0.0559080	+	0.122422i
$902$	−43.9215	+	12.8965i	−1.46243	+	0.429407i
$903$	−20.2029	−	10.7931i	−0.672312	−	0.359172i
$904$	−6.86457	+	5.94818i	−0.228312	+	0.197834i
$905$	−23.9345	+	3.44127i	−0.795611	+	0.114392i
$906$	1.70674	+	4.45125i	0.0567026	+	0.147883i
$907$	4.18175	+	3.62351i	0.138853	+	0.120317i	0.721518	−	0.692396i	$-0.243445\pi$
$907$	4.18175	+	3.62351i	0.138853	+	0.120317i	−0.582665	+	0.812712i	$0.697990\pi$
$908$	−14.3822	−	9.24291i	−0.477292	−	0.306737i
$909$	−5.88734	−	6.54854i	−0.195271	−	0.217201i
$910$	1.42974	−	1.65001i	0.0473953	−	0.0546971i
$911$	−13.0459	−	3.83063i	−0.432231	−	0.126915i	0.0583773	−	0.998295i	$-0.481407\pi$
$911$	−13.0459	−	3.83063i	−0.432231	−	0.126915i	−0.490609	+	0.871380i	$0.663226\pi$
$912$	−0.901805	+	0.918444i	−0.0298617	+	0.0304127i
$913$	−3.72914	−	4.30366i	−0.123417	−	0.142430i
$914$	6.84875	+	14.9967i	0.226536	+	0.496046i
$915$	−16.6781	−	12.2488i	−0.551360	−	0.404932i
$916$	10.9789	+	5.01389i	0.362753	+	0.165664i
$917$	−3.01766	+	20.9883i	−0.0996518	+	0.693093i
$918$	1.98221	−	2.80507i	0.0654228	−	0.0925813i
$919$		−	47.2119i		−	1.55738i	−0.627411	−	0.778688i	$-0.715886\pi$
$919$		−	47.2119i		−	1.55738i	0.627411	−	0.778688i	$-0.284114\pi$
$920$	−4.55660	+	1.49579i	−0.150227	+	0.0493149i
$921$	−8.40745	+	6.41448i	−0.277035	+	0.211364i
$922$	8.76297	−	5.63162i	0.288593	−	0.185468i
$923$	10.7937	+	1.55190i	0.355278	+	0.0510813i
$924$	13.3338	−	3.02850i	0.438651	−	0.0996304i
$925$	−1.03825	−	3.53595i	−0.0341374	−	0.116261i
$926$	−3.57164	+	1.63111i	−0.117371	+	0.0536018i
$927$	2.63305	+	5.49736i	0.0864809	+	0.180557i
$928$	1.02058	+	7.09832i	0.0335023	+	0.233014i
$929$	4.72546	−	16.0934i	0.155037	−	0.528008i	−0.844939	−	0.534862i	$-0.820364\pi$
$929$	4.72546	−	16.0934i	0.155037	−	0.528008i	0.999977	+	0.00685406i	$0.00218173\pi$
$930$	−9.79159	−	0.610406i	−0.321079	−	0.0200160i
$931$	1.06211	−	1.65268i	0.0348093	−	0.0541643i
$932$	−11.1177	+	17.2995i	−0.364172	+	0.566663i
$933$	−22.6960	−	1.41486i	−0.743033	−	0.0463205i
$934$	6.76193	−	23.0290i	0.221257	−	0.753533i
$935$	−0.355808	−	2.47470i	−0.0116362	−	0.0809314i
$936$	−1.35556	−	2.83018i	−0.0443080	−	0.0925073i
$937$	−25.2230	+	11.5189i	−0.823999	+	0.376308i	−0.782361	−	0.622825i	$-0.785985\pi$
$937$	−25.2230	+	11.5189i	−0.823999	+	0.376308i	−0.0416377	+	0.999133i	$0.513258\pi$
$938$	2.03241	+	6.92174i	0.0663604	+	0.226003i
$939$	−14.6500	+	3.32745i	−0.478086	+	0.108587i
$940$	−2.62482	−	0.377393i	−0.0856123	−	0.0123092i
$941$	−18.9966	+	12.2084i	−0.619271	+	0.397981i	−0.812323	−	0.583207i	$-0.801798\pi$
$941$	−18.9966	+	12.2084i	−0.619271	+	0.397981i	0.193053	+	0.981188i	$0.438161\pi$
$942$	−5.45962	+	4.16543i	−0.177884	+	0.135717i
$943$	−10.0707	−	57.1625i	−0.327946	−	1.86147i
$944$		−	9.09955i		−	0.296165i
$945$	−6.25895	+	8.85718i	−0.203604	+	0.288124i
$946$	−3.41043	+	23.7201i	−0.110883	+	0.771206i
$947$	34.1596	+	15.6002i	1.11004	+	0.506937i	0.884144	−	0.467215i	$-0.154742\pi$
$947$	34.1596	+	15.6002i	1.11004	+	0.506937i	0.225894	+	0.974152i	$0.427470\pi$
$948$	−9.13822	−	6.71133i	−0.296796	−	0.217974i
$949$	−5.03707	−	11.0296i	−0.163510	−	0.358037i
$950$	−0.486656	−	0.561631i	−0.0157892	−	0.0182217i
$951$	36.8551	−	37.5351i	1.19511	−	1.21716i
$952$	1.32380	+	0.388703i	0.0429047	+	0.0125980i
$953$	−14.7151	+	16.9822i	−0.476670	+	0.550107i	−0.942255	−	0.334896i	$-0.891299\pi$
$953$	−14.7151	+	16.9822i	−0.476670	+	0.550107i	0.465585	+	0.885003i	$0.345844\pi$
$954$	−12.2576	−	13.6342i	−0.396854	−	0.441424i
$955$	−6.08170	−	3.90847i	−0.196799	−	0.126475i
$956$	5.12313	+	4.43922i	0.165694	+	0.143575i
$957$	−16.8194	−	43.8657i	−0.543694	−	1.41798i
$958$	16.6604	−	2.39540i	0.538273	−	0.0773919i
$959$	−6.34840	+	5.50092i	−0.205000	+	0.177634i
$960$	−1.52771	−	0.816154i	−0.0493066	−	0.0263412i
$961$	−1.03876	+	0.305007i	−0.0335084	+	0.00983894i
$962$	1.60135	−	3.50648i	0.0516298	−	0.113053i
$963$	19.6155	+	8.52826i	0.632101	+	0.274819i
$964$	16.3601	+	25.4568i	0.526924	+	0.819910i
$965$	24.0832			0.775266
$966$	1.93996	+	17.2288i	0.0624172	+	0.554327i
$967$	−18.8261			−0.605406			−0.302703	−	0.953085i	$-0.597889\pi$
$967$	−18.8261			−0.605406			−0.302703	+	0.953085i	$0.597889\pi$
$968$	−1.78706	−	2.78073i	−0.0574384	−	0.0893759i
$969$	0.743008	−	0.414574i	0.0238689	−	0.0133180i
$970$	6.68889	−	14.6466i	0.214767	−	0.470275i
$971$	−39.9729	+	11.7371i	−1.28279	+	0.376662i	−0.850930	−	0.525279i	$-0.823961\pi$
$971$	−39.9729	+	11.7371i	−1.28279	+	0.376662i	−0.431861	+	0.901940i	$0.642143\pi$
$972$	8.08803	+	13.3261i	0.259424	+	0.427433i
$973$	16.1983	−	14.0359i	0.519292	−	0.449969i
$974$	35.0235	−	5.03562i	1.12223	−	0.161352i
$975$	1.69167	−	0.648637i	0.0541769	−	0.0207730i
$976$	−9.02893	−	7.82361i	−0.289009	−	0.250428i
$977$	−13.5596	−	8.71426i	−0.433812	−	0.278794i	0.305455	−	0.952206i	$-0.401191\pi$
$977$	−13.5596	−	8.71426i	−0.433812	−	0.278794i	−0.739267	+	0.673413i	$0.764828\pi$
$978$	0.320528	+	3.97110i	0.0102493	+	0.126982i
$979$	−20.0701	+	23.1621i	−0.641443	+	0.740265i
$980$	2.53647	+	0.744775i	0.0810246	+	0.0237910i
$981$	1.31765	−	10.5272i	0.0420693	−	0.336108i
$982$	−20.0461	−	23.1344i	−0.639697	−	0.738249i
$983$	−9.68598	−	21.2093i	−0.308935	−	0.676473i	0.689942	−	0.723865i	$-0.257636\pi$
$983$	−9.68598	−	21.2093i	−0.308935	−	0.676473i	−0.998876	+	0.0473923i	$0.984909\pi$
$984$	12.4085	−	16.8955i	0.395569	−	0.538610i
$985$	10.2337	+	4.67357i	0.326073	+	0.148912i
$986$	0.674628	−	4.69214i	0.0214845	−	0.149428i
$987$	−3.26797	+	9.01252i	−0.104021	+	0.286872i
$988$		−	0.777346i		−	0.0247307i
$989$	−29.4109	−	7.63565i	−0.935211	−	0.242800i
$990$	10.9438	+	2.99720i	0.347816	+	0.0952573i
$991$	−50.8887	+	32.7042i	−1.61653	+	1.03888i	−0.658354	+	0.752709i	$0.728747\pi$
$991$	−50.8887	+	32.7042i	−1.61653	+	1.03888i	−0.958178	+	0.286173i	$0.907617\pi$
$992$	−5.60650	−	0.806093i	−0.178007	−	0.0255935i
$993$	−0.347107	−	1.52823i	−0.0110151	−	0.0484971i
$994$	−6.13020	−	20.8776i	−0.194438	−	0.662196i
$995$	1.76574	−	0.806388i	0.0559779	−	0.0255642i
$996$	2.55314	+	0.531008i	0.0808993	+	0.0168256i
$997$	7.87158	+	54.7480i	0.249295	+	1.73389i	0.602304	+	0.798267i	$0.294250\pi$
$997$	7.87158	+	54.7480i	0.249295	+	1.73389i	−0.353009	+	0.935620i	$0.614841\pi$
$998$	−0.717432	+	2.44335i	−0.0227099	+	0.0773429i
$999$	−6.19744	+	18.1184i	−0.196078	+	0.573240i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.q.a.11.14	✓	160
3.2	odd	2		690.2.q.b.11.2	yes	160
23.21	odd	22		690.2.q.b.251.2	yes	160
69.44	even	22	inner	690.2.q.a.251.14	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.q.a.11.14	✓	160	1.1	even	1	trivial
690.2.q.a.251.14	yes	160	69.44	even	22	inner
690.2.q.b.11.2	yes	160	3.2	odd	2
690.2.q.b.251.2	yes	160	23.21	odd	22

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.q (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.540641 + 0.841254i) q^{2} +(0.843944 + 1.51253i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.816154 + 1.52771i) q^{6} +(-1.57741 + 1.36683i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(-1.57552 + 2.55299i) q^{9} +O(q^{10})\)	\(q+(0.540641 + 0.841254i) q^{2} +(0.843944 + 1.51253i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.816154 + 1.52771i) q^{6} +(-1.57741 + 1.36683i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(-1.57552 + 2.55299i) q^{9} +(-0.755750 - 0.654861i) q^{10} +(3.18184 + 2.04484i) q^{11} +(-1.72644 + 0.139349i) q^{12} +(0.684999 - 0.790531i) q^{13} +(-2.00266 - 0.588035i) q^{14} +(-1.23589 - 1.21350i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(0.274598 + 0.601286i) q^{17} +(-2.99950 + 0.0548407i) q^{18} +(-0.675988 - 0.308713i) q^{19} +(0.142315 - 0.989821i) q^{20} +(-3.39862 - 1.23235i) q^{21} +3.78226i q^{22} +(-4.76620 - 0.532257i) q^{23} +(-1.05061 - 1.37703i) q^{24} +(0.841254 - 0.540641i) q^{25} +(1.03538 + 0.148865i) q^{26} +(-5.19113 - 0.228443i) q^{27} +(-0.588035 - 2.00266i) q^{28} +(-6.52326 + 2.97907i) q^{29} +(0.352688 - 1.69576i) q^{30} +(-0.806093 - 5.60650i) q^{31} +(0.281733 - 0.959493i) q^{32} +(-0.407600 + 6.53837i) q^{33} +(-0.357375 + 0.556086i) q^{34} +(1.12843 - 1.75587i) q^{35} +(-1.66779 - 2.49369i) q^{36} +(1.03825 - 3.53595i) q^{37} +(-0.105760 - 0.735580i) q^{38} +(1.77381 + 0.368920i) q^{39} +(0.909632 - 0.415415i) q^{40} +(3.40974 + 11.6125i) q^{41} +(-0.800713 - 3.52537i) q^{42} +(6.27140 + 0.901692i) q^{43} +(-3.18184 + 2.04484i) q^{44} +(0.792437 - 2.89345i) q^{45} +(-2.12904 - 4.29735i) q^{46} -2.65181i q^{47} +(0.590431 - 1.62831i) q^{48} +(-0.376217 + 2.61665i) q^{49} +(0.909632 + 0.415415i) q^{50} +(-0.677719 + 0.922790i) q^{51} +(0.434534 + 0.951496i) q^{52} +(4.00210 + 4.61867i) q^{53} +(-2.61436 - 4.49056i) q^{54} +(-3.62905 - 1.06558i) q^{55} +(1.36683 - 1.57741i) q^{56} +(-0.103557 - 1.28299i) q^{57} +(-6.03290 - 3.87711i) q^{58} +(6.87698 + 5.95894i) q^{59} +(1.61724 - 0.620098i) q^{60} +(11.8254 - 1.70023i) q^{61} +(4.28068 - 3.70923i) q^{62} +(-1.00427 - 6.18057i) q^{63} +(0.959493 - 0.281733i) q^{64} +(-0.434534 + 0.951496i) q^{65} +(-5.72079 + 3.19201i) q^{66} +(-1.86860 - 2.90760i) q^{67} -0.661021 q^{68} +(-3.21735 - 7.65824i) q^{69} +2.08721 q^{70} +(5.63612 + 8.76998i) q^{71} +(1.19615 - 2.75122i) q^{72} +(4.81545 - 10.5444i) q^{73} +(3.53595 - 1.03825i) q^{74} +(1.52771 + 0.816154i) q^{75} +(0.561631 - 0.486656i) q^{76} +(-7.81401 + 1.12348i) q^{77} +(0.648637 + 1.69167i) q^{78} +(4.94711 + 4.28670i) q^{79} +(0.841254 + 0.540641i) q^{80} +(-4.03550 - 8.04455i) q^{81} +(-7.92562 + 9.14666i) q^{82} +(-1.44461 - 0.424176i) q^{83} +(2.53283 - 2.57956i) q^{84} +(-0.432877 - 0.499566i) q^{85} +(2.63203 + 5.76333i) q^{86} +(-10.0112 - 7.35248i) q^{87} +(-3.44046 - 1.57121i) q^{88} +(-1.15319 + 8.02060i) q^{89} +(2.86255 - 0.897676i) q^{90} +2.18327i q^{91} +(2.46411 - 4.11438i) q^{92} +(7.79972 - 5.95081i) q^{93} +(2.23085 - 1.43368i) q^{94} +(0.735580 + 0.105760i) q^{95} +(1.68903 - 0.383629i) q^{96} +(4.53637 + 15.4495i) q^{97} +(-2.40466 + 1.09817i) q^{98} +(-10.2335 + 4.90151i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9}+O(q^{10}) \) 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9	\( 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9} - 12 q^{11} - 12 q^{14} - 16 q^{16} - 8 q^{18} + 16 q^{20} + 62 q^{21} + 4 q^{23} + 2 q^{24} - 16 q^{25} + 42 q^{27} - 2 q^{30} - 4 q^{31} + 16 q^{33} + 2 q^{36} + 72 q^{38} - 124 q^{39} + 44 q^{41} + 44 q^{43} + 12 q^{44} - 2 q^{45} + 4 q^{46} + 70 q^{49} - 2 q^{51} - 52 q^{53} + 92 q^{54} + 10 q^{55} - 54 q^{56} - 38 q^{57} - 36 q^{58} - 44 q^{61} - 220 q^{63} + 16 q^{64} - 34 q^{66} - 44 q^{67} + 22 q^{69} - 12 q^{70} - 36 q^{72} - 28 q^{73} - 24 q^{74} - 88 q^{77} - 54 q^{78} - 44 q^{79} - 16 q^{80} - 66 q^{81} - 28 q^{82} + 4 q^{83} - 18 q^{84} + 158 q^{86} - 64 q^{87} + 80 q^{89} - 8 q^{90} - 4 q^{92} + 4 q^{93} + 24 q^{94} - 2 q^{96} - 88 q^{98} + 190 q^{99}+O(q^{100}) \) 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9 - 12 * q^11 - 12 * q^14 - 16 * q^16 - 8 * q^18 + 16 * q^20 + 62 * q^21 + 4 * q^23 + 2 * q^24 - 16 * q^25 + 42 * q^27 - 2 * q^30 - 4 * q^31 + 16 * q^33 + 2 * q^36 + 72 * q^38 - 124 * q^39 + 44 * q^41 + 44 * q^43 + 12 * q^44 - 2 * q^45 + 4 * q^46 + 70 * q^49 - 2 * q^51 - 52 * q^53 + 92 * q^54 + 10 * q^55 - 54 * q^56 - 38 * q^57 - 36 * q^58 - 44 * q^61 - 220 * q^63 + 16 * q^64 - 34 * q^66 - 44 * q^67 + 22 * q^69 - 12 * q^70 - 36 * q^72 - 28 * q^73 - 24 * q^74 - 88 * q^77 - 54 * q^78 - 44 * q^79 - 16 * q^80 - 66 * q^81 - 28 * q^82 + 4 * q^83 - 18 * q^84 + 158 * q^86 - 64 * q^87 + 80 * q^89 - 8 * q^90 - 4 * q^92 + 4 * q^93 + 24 * q^94 - 2 * q^96 - 88 * q^98 + 190 * q^99

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